Practice A Slope-Intercept Form Find the x- and y-intercepts. 1. y 3x 6. y x 8 _ Graph each equation. 3. y 1 x 3 4. y 5x 5 5. y x 4 Write the equation of the line in slope-intercept form. 6. 7. _
Practice B Slope-Intercept Form Find the x- and y-intercepts. 1. y 1 1 4 x 10. y 3 x 8 _ Graph each equation. 3. y 1 1 3 x 4. y x 1 5. y 1 3 7 x 9 Write the equation of the line in slope-intercept form. 6. 7.
Practice C Slope-Intercept Form Find the x- and y-intercepts. 1. y 9 6 x 18. y 3 3 8 x 108 _ Graph each equation. 3. y 0.3x 3.5 4. y 4 5 7 x 99 5. y 350 14 x 75 Write the equation of the line in slope-intercept form. 6. 7.
Review for Mastery Slope-Intercept Form Look at the three graphed lines below. How are lines A and B alike? How are lines A and C alike? Lines A and B have the same steepness, or slope. Lines A and C both go through the same point on the y-axis, (0, 0). This information is shown by equations in slope-intercept form. Slope-intercept form shows the slope of a line, the direction the line slopes, and where the line crosses the y-axis. Equation for Slope-Intercept Form y mx b slope y-intercept 3 The equation for line B in slope-intercept form is y x The number 3 is the slope. If you start at any point on line B, and move up 3 units and to the right units, you will end at another point on line B. Count the line s rise and run for yourself. Since 3 is positive, you know that the direction of slope for Line B is positive. This means the line slopes upward. The negative sign in front of the number tells you the line crosses the y-axis at. This is the y-intercept. Use the graph to answer the questions. 1. At what point does the line cross the y-axis? What is the ordered pair for this point?. How can you find the slope of the line? 3. What is the slope of this line? 4. Write an equation for this line in slope intercept-form.
Challenge Point-Slope Form Another way of writing the equation for a line is known as point-slope form. The equation for point-slope form is y y 1 m(x x 1 ), where m is the slope of the line and (x 1, y 1 ) is any point on the line. Point-slope form can help you write other forms of the equation. A line with a slope of 4 that passes through (, ) is written in pointslope form as y 4(x ). Applying the Distributive Property of multiplication to the right side gives y 4x 8. Adding to both sides gives you: y 4x 8 y 4x 6 The graph of the line is shown. 1. Use point-slope form to graph a line that has the point ( 3, 1) and a slope of. Include the steps 3 you used in your solution.. A line has a slope of 1 1. One point on the line is (4, 6). Will the line go through the origin, (0,0)? Explain your answer. 3. Use point-slope form to graph the line indicated in Exercise. Show the steps in your solution.
Problem Solving Slope-Intercept Form Write the correct answer. Insulation is sold in 10 15 ft sheets that cost $79.50 each. A job requires 900 ft of insulation to be installed. 1. Let y be the number of square feet of insulation to be installed, and x be the total amount paid. Write an equation in slope-intercept form to express the relation between remaining insulation and total cost.. What is the slope of the function? 3. What is the y-intercept, and what does it represent? Choose the letter for the best answer. The drawing shows a partial blueprint for a pitched roof. The height of the roof is 1 3 the length from the gutter to point A. 4. What is the slope of the roof? A m = 3 J y 1 3 x 14 B m = 1 3 C m = 1 3 D There is no way to tell. 5. If the height of the roof is 14 feet, what is the equation of the line? F y 1 3 x 14 G 3y = 3x 14 H y 14 3 x 1 6. If the equation for the roof were graphed, which would be a point on the graph? A (0, 3) B (0, 0) C (3, 13) D (3, 1)
Reading Strategies Use Graphs and Equations to Understand Slope-Intercept Form The graph of a line reveals information about the line. It tells the line s slope its rise over its run. It tells the direction of slope whether the line slopes up or down. It also tells the y-intercept the point where the line crosses the y-axis. The slope-intercept form (y mx b) gives the same information. + or tells whether the line slopes up or down. In this case it slopes down. (Remember, no sign at all means +.) + or tells whether the y-intercept is above the x-axis (greater than 0) or below the x-axis (less than 0). In this case, the y-intercept is above the x-axis. y x 4 The slope, or degree of steepness of the line. The numerator is rise, up and down change. The denominator is run, side to side change. In this case, the slope of the line is, or. The line goes down grid 1 The y-intercept, the point where the line crosses the y-axis. Its sign tells whether it is above or below the x-axis. In this case, the y- intercept of the line occurs 4 grid lines above the y-axis. lines and to the right 1 grid line. Use the three equations below to answer the questions. A. y 3 4 x 3 B. y 1 x 1 C. y 4x 8 5 1. What is the y-intercept of the line in equation A?. What is the slope of the line in equation C? 3. Which equation does not have a y-intercept that is above the x- axis? 4. Which equation does not have a negative slope? 5. Which equation has a slope whose rise is 1 and whose run is 5? 6. What number represents the slope of the line in equation C? 7. Which equation is for a line that crosses the y-axis at 8?
Puzzles, Twisters & Teasers Home Away from Home Below are six linear equations, each followed by special instructions in italics. Graph each equation, and follow the instructions. If done correctly, the graphed line segments will form a place you might stay while camping. Write the type of structure shown in the space below the graph. (Note: Be sure to work in pencil in case you need to erase!) A. y x 3 Start the line segment where x 4, and end it where x 0 B. y 3x Draw the line segment from the y-intercept to where x 1 C. y 5 Begin the line segment from x 4 to x 1. D. y 5 Extend the line segment at x 1 and end at x 4. E. y 3x Draw the line segment from the y-intercept to where y 5 F. y 4 x 3 Start the line segment from where y 3 to where y 5 The type of camp structure
LESSON 5-7 3. Practice A 1. x-intercept, y-intercept 6. x-intercept 4, y-intercept 8 3. 4. 4. 5. 5. 1 5 6. y 1 x 1 7. y x 5 7 6 Practice C 1. x-intercept 1, y-intercept 18. x-intercept 3, y-intercept 108 3. 6. y x 4 7. y 1 3 x 1 Practice B 1. x-intercept 8, y-intercept 10. x-intercept 3, y-intercept 8
4.. Yes. The equation in point-slope form 5. is y 6 1 1 (x 4), which can be written in slope-intercept form as y 1 1 x. When you use the point (0,0), the equation is true, so the line crosses through the point (0,0). 3. y y 1 m(x x 1 ) y 6 1 1 (x 4) y 6 1 1 x 6 10 6. y x 1 3 7. y 50 x Review for Mastery 1. At point B; (0, ). Possible answer: To find the slope, find the ratio of rise to run. 3. 4. y x Challenge 1. y y 1 m(x x 1 ) y 1 (x 3) 3 1 1 y 3 x 3 y 6 6 1 1 x Problem Solving 1. y 150 79.50 x 900. 150 79.50 3. The y-intercept represents the number of square feet of insulation still needed.
4. B 5. D 6. C Reading Strategies 1. 3. 4 3. B 4. A 5. B 6. 4 7. C Puzzles, Twisters & Teasers tent