Slope. Plug In. Finding the Slope of a Line. m 5 1_ 2. The y-intercept is where a line

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LESSON Slope Plug In Finding the Slope of a Line The slope of a line is the ratio of the change in the -values to the change in the corresponding -values.

The -intercept is where a line crosses the -ais. (0, ) -intercept is. 0 7 8 The -intercept is the -coordinate of the point where the line intersects the -ais.

The slope is m _, and the -intercept is b, so the equation of the line is _.

1 LESSON Slope Plug In Finding the Slope of a Line The slope of a line is the ratio of the change in the -values to the change in the corresponding -values change in -values Slope change in -values 8 I see! I choose two coordinate pairs and then divide the difference of the -values b the difference of the corresponding -values. The -intercept is where a line crosses the -ais. (0, ) -intercept is The -intercept is the -coordinate of the point where the line intersects the -ais. The equation of a line can be written in the form m b, where the slope of the line is m, and the -intercept is b. (0, ) I get it! The slope is m _, and the -intercept is b, so the equation of the line is _. Words to Know slope a ratio of the change in -coordinates (rise) of a graph to the change in corresponding -coordinates (run) -intercept the -coordinate of the point at which a line crosses the -ais Will the slope of the line through the points (, ) and (7, ) be positive or negative? How do ou know? A You can use the slope formula m to find the slope of a line. Find the slope of the line through points (, ) and (, ). Choose (, ) and (, ). Write the slope formula. Substitute for,,, and. Subtract. Simplif, if possible. (, ) (, ) (, ) (, ) slope Duplicating an part of this book is prohibited b law. 0 Triumph Learning, LLC Lesson

2 Slope B You can use the equation of a line to find its slope and -intercept. Find the slope and -intercept of the line with the equation. Compare the equation of the given line to m b. Identif the slope, m, and the -intercept, b. m b m b The slope of the line is. The -intercept of the line is. I have to make sure the equation of a line is in the form m b to determine the slope and -intercept. Wh do ou think the slope of a vertical line is described as undefined? Eplain b computing the slope of the vertical line through points (, ) and (, ). PRACTICE Find the slope of the line that contains the given points. (, ) and (, ) m (, ) and (, ) m Duplicating an part of this book is prohibited b law. 0 Triumph Learning, LLC Find the slope and -intercept of each line. 0 slope -intercept slope -intercept 0 slope -intercept slope -intercept

Identif where the line crosses the -ais. The line crosses the -ais at (0, ). 0 I see! If I know the slope and -intercept of a line, then I can write an equation for the line. The -intercept is.

3 POWER UP Writing an Equation of a Line You can write the equation of a line from its graph using the form m b. Find the slope. Choose two points on the line, and use the slope formula to calculate the slope. Using the points (, ) and (, ): change in -values m change in -values () () Find the -intercept. Identif where the line crosses the -ais. The line crosses the -ais at (0, ). 0 I see! If I know the slope and -intercept of a line, then I can write an equation for the line. The -intercept is. Substitute the slope, m, and the -intercept, b, in the equation m b. m b is an equation for the line. The and in the equation represent all the possible coordinate pairs of points on the line. A Does the slope change, depending on which point ou assign as (, ) or (, )? Eplain. You can write the equation of a line if given the slope and -intercept. What is the equation of a line that has a slope of 8 and a -intercept of. Identif m and b. Substitute the slope, m, and the -intercept, b, in the equation m b. Write the equation. m b m b I remember! m stands for slope and b represents the -intercept. Duplicating an part of this book is prohibited b law. 0 Triumph Learning, LLC Lesson

4 Slope B You can write the equation of a line that passes through the origin. Write an equation for the line shown in the graph. Choose two points on the line. Find the slope. m Identif the -intercept. Write the equation. Simplif, if possible. (, ) (, ) (, ) (, ) m 0 The line crosses the -ais at the origin. So b. I remember! The coordinates of the origin are represented b the point (0,0). Andrew sas that he can use the form b to write the equation for an horizontal line that passes through the point (0, b). Is Andrew correct? Eplain. Duplicating an part of this book is prohibited b law. 0 Triumph Learning, LLC PRACTICE Write the equation for the line. 0 Write an equation of the line with the given slope and -intercept. 0 slope ; -intercept 7 slope ; -intercept Write an equation of the line that passes through the given points. (0, ) and (, ) (0, ) and (, ) I remember! All horizontal lines have a slope of 0. That means m 0 for all horizontal lines. 7

5 READY TO GO Slope You can use an two points on a line to find the slope of the line. You can compare the slopes of two segments of the line to show this. Use the points (0, ) and (, ) to find the slope of the line. m () 0 Use the points (, ) and (9, ) to find the slope of the line. m () 9 Compare the slopes. The slopes are equal. I get it! Ever segment of a line will have the same slope! Margarita looks at a table of - values and calculates the slope using one pair of points. She uses another pair of points and calculates a different slope. What can Margarita conclude about a graph of those points? lesson link Plug In POWER UP GO! You can find the slope and -intercept of a line given an two points on the line, its graph, or its equation. slope: m 0 -intercept: b You can use the slope and -intercept of a line to write an equation for the line. Slope: m 8 -intercept: b m b 8 () 8 I get it! I can investigate slope and -intercept further to better understand the characteristics of lines! Duplicating an part of this book is prohibited b law. 0 Triumph Learning, LLC 8 Lesson

6 work together Use two pairs of points to confirm the slope of a line. This line includes the points (, ), (, ), (, 0), and (, ). The slope between (, ) and (, ) is, or. The slope between (, 0) and (, ) is, or. The slope of the line is the same with either pair of points. 0 Slope I could also use an other two pairs of points on this line to confirm the slope. A You can use slope to check whether three points lie on the same line. Determine if the points (0, ), (, ), and (, ) are on the same line. Find the slope between an two of the three points. Now find the slope between two other points. Compare the slopes to determine if the points are on the same line. Use (0, ) and (, ). m Use (, ) and (, ). m The three points on the same line because the slopes are. Duplicating an part of this book is prohibited b law. 0 Triumph Learning, LLC B You can determine if two segments that share an endpoint are on the same line. Determine if two segments, one with endpoints (0, ) and (, ) and one with endpoints (0, ) and (8, ), lie along the same line. Find the slope of the first segment. Find the slope of the second segment. Compare the slopes to determine if the are on the same line. Use (0, ) and (, ). m Now use (0, ) and (8, ). m The slopes are. The points on the same line. Will a line segment that is part of a larger line segment alwas have the same slope as the larger line segment? Eplain. 9

7 Read to Go practice Solve. A line segment has endpoints at (, ) and (, ). Another line segment has endpoints at (, ) and (, 7). Are the line segments parts of the same line? Find the slope of the first line segment. m () Find the slope of the second line segment. m Are the line segments on the same line? Eplain. Coordinate Grid can be found on p. HINT You can check our answer b graphing the segments on a coordinate grid. Choose two pairs of points on the line to show the slope of the line is the same. Use points (, ) and (, ). m 0 REMEMBER An two pairs of points on the line will show the same slope. Now use points (, ) and (, ). m Are the slopes the same? Use the endpoints of two segments along this line to show that the slopes of the segments are the same. Are the slopes of the segments the same? 0 Duplicating an part of this book is prohibited b law. 0 Triumph Learning, LLC 0 Lesson

Slope Solve. Two line segments are part of the line 0. What is the slope of each segment? Barb drew a line through the origin and point (, ). Jamal drew a line through the origin and point (, ).

8 Slope Solve. Two line segments are part of the line 0. What is the slope of each segment? Barb drew a line through the origin and point (, ). Jamal drew a line through the origin and point (, ). How can ou tell that Barb and Jamal drew the same line? Use the slope formula to determine if the three points lie on a line. (, ), (, ), (, ) I see! I can think of an two points as the endpoints of a segment. Do the points lie on the same line? Eplain. 7 (, ), (, 7), (, ) Do the points lie on the same line? Eplain. Duplicating an part of this book is prohibited b law. 0 Triumph Learning, LLC Reasoning with Graphs Do an segments within each of these graphs share an endpoint? Eplain. 0 m 0 What do ou notice about the slopes as the lines gets steeper? 0 m m I get it! I can relate the steepness of a line with the value of its slope.

9 Read to Go Problem solving READ PLAN Underwater Pressure The units of measure for pressure are called atmospheres. The pressure at sea level is atmosphere. At a depth of 0 meters, the pressure is atmospheres. Write an equation, and find the pressure at a depth of 00 meters. You need to find the number of atmospheres at a depth of. Use (0, ) for the pressure at. Use for the pressure at a depth of 0 meters. Use the points to find the. Use the measure of pressure at as the -intercept. Use m b and substitute for. SOLVE Write an equation. The slope, m CHECK The -intercept is. The equation is. Find the number of atmospheres at a depth of 00 meters: 0 ( ) Write an ordered pair for the atmosphere at a depth of 00 meters. (00, ) Check that this point and the given two points lie on the same line. The slope between (0, ) and (0, ) is. The slope between (0, ) and (00, ) is: m The slopes are, so the points. At a depth of 00 meters, the pressure is atmospheres. Duplicating an part of this book is prohibited b law. 0 Triumph Learning, LLC Lesson

10 Slope practice Use the problem-solving steps to help ou. A computer repair compan charges $0 for an appointment. For hours of repair work, it charges a total of $0. What is the total charge for hours of repair work? I see! For the compan to perform an repair work, a customer is charged for making an appointment. That amount is the -intercept! CHECKLIST Read Plan Solve Check At dawn, the temperature is 70 F. The temperature falls at the same rate for the rest of the da. In hours, the temperature is 0 F. What is the temperature hours after dawn? CHECKLIST Read Plan Solve Check Duplicating an part of this book is prohibited b law. 0 Triumph Learning, LLC Jennie works for a cell phone compan. She earns $0 per week plus commissions she makes on sales. One week, she had sales of $000, and her pa was $7. How much would her pa be if she had sales of $,000? CHECKLIST Read Plan Solve Check

4.5 Equations of Parallel and Perpendicular Lines

4.5 Equations of Parallel and Perpendicular Lines Name Class Date.5 Equations of Parallel and Perpendicular Lines Essential Question: How can ou find the equation of a line that is parallel or perpendicular to a given line? Resource Locker Eplore Eploring