Answer the following: 1.Find the slope and y-intercept of the given function y=

Question

Answer the following:

1.Find the slope and y-intercept of the given function y= -3x + 15
2.Find the slope, if it exists, of the line containing the points (12,5) and (8,-6)
3.Find the linear function y=mx+b whose graph has the given slope of 5.2 and y-intercept (0,-4)
4.Determine the equation of the line that is parallel to the line 12x-3y=6 and passes through the point (5,1)
5.Explain the usefulness of the slope concept when describing a line.
6.Alvin has been employed with Univ.of College Sucess and Excellent Pay for several years. Throughout the years has receieved several pay increases and raises because of his hard work and dedication. In 1990, alvin's starting salary was 35,000. Currently (2010), Alvin is making 95,000 per year. If we use a straight line appreciation model, what is the linear equation that approximates Alvin's salary.

Explanation / Answer

1. The slope of the function given is just the term in multiplied by x, which is -3. The y-intercept is just the constant term in the function, which is +15

2. Slope is just rise over run which is the vertical distance from point one to point two divided by the horizontal distance from point one to point two. Therefore, slope = (y1-y2)/(x1-x2) = (5-(-6))/(12-8) = 11/2

3. slope = m and y-intercept = b, there fore y = (11/2)*x -4

4. Since the line is parallel, the slope is the same. Slope =12/3 = 4. When y = 1, and x = 5, b = -19. Therefore, y = 4x -19

5. The slope concept allows for the determination of the equation of the line and.....

6. Intial point of pay (0 yrs, 35,000) Final point of pay (20 yrs, 95,000). So the slope of the equation is the rise over the run which is (35000-95000)/(0-20) = (-60,000)/(-20) = 6,000/2 = 3,000. THe y-intercept is wher the line crosses the y-axis which is 35,000.

so y = 3,000*x + 35,000

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