Math 1023 College Algebra Worksheet 1 Name: Prof. Paul Bailey September 22, 2004
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1 Math 1023 College Algebra Worksheet 1 Name: Prof. Paul Bailey September 22, 2004 Every vertical line can be expressed by a unique equation of the form x = c, where c is a constant. Such lines have undefined slope (or, one may say that the slope is ). Every other line has can be expressed by a unique equation of the form y = mx + b. This is called slope-intercept form, where m is the slope and b is the y-value of the y intercept. Example 1. Consider the graph of a line. Find the standard form (y = mx + b) of the line, and identify Solution. By examining the graph, we see that the y-intercept of the line is (0, 5) and that the x-intercept is (3, 0). The slope is the change in y divided by the change in x, which is 5 3. Thus m = 5 3 and b = 5. y = 5 3 x 5 m: 5 3 b: (0, 5) (3, 0) Problem 1. Consider the graph of a line. Find the standard form (y = mx + b) of the line, and identify
2 Problem 2. Consider the graph of a line. Find the standard form (y = mx + b) of the line, and identify Problem 3. Consider the graph of a line. Find the standard form (y = mx + b) of the line, and identify
3 Problem 4. Consider the graph of a line. Find the standard form (y = mx + b) of the line, and identify Problem 5. Consider the graph of a line. Find the standard form (y = mx + b) of the line, and identify
4 Example 2. Consider the equation 3x + 6y = 9. Find the standard form (y = mx + b) of the line, and identify Graph the line and label these points. Solution. First we must solve for y. Subtract 3x from both sides to get 6y = 3x + 9. Divide by 6 to get y = 1 2 x Thus m = 1 2 and b = 3 2. The slope is the number in front of the x when the equation is in slope-intercept form (that is, the slope is m). In this case, the slope is 1 2. This is negative, so the graph goes down. The y-intercept is the point where the line intersects the y-axis. This is obtained by plugging in 0 for x, and solving for y. In this case, we obtain y = 3 2. The the y-intercept is the point (0, 3 2 ). The x-intercept is the point where the line intersects the x-axis. This is obtained by plugging in 0 for y and solving for x. In this case, we obtain x = 3. Thus the x-intercept is the point (3, 0). Equation: 3x + 6y = 9 y = 1 2 x m: 1 2 b: (0, 3 2 ) (3, 0) Problem 6. Consider the equation y = 2x 3. Find the standard form (y = mx+b) of the line, and identify Graph the line and label these points. Equation: y = 2x 3
5 Problem 7. Consider the equation 4x 3y = 12. Find the standard form (y = mx + b) of the line, and identify Graph the line and label these points. Equation: 4x 3y = 12 Problem 8. Consider the equation y = 3. Find the standard form (y = mx + b) of the line, and identify Graph the line and label these points. Equation: y = 3
6 Problem 9. Consider the equation 7y = 49 14x. Find the standard form (y = mx + b) of the line, and identify Graph the line and label these points. Equation: 7y = 49 14x Problem 10. Consider the equation x y = 2. Find the standard form (y = mx + b) of the line, and identify Graph the line and label these points. Equation: x y = 2
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