Question

When graphing, what is the starting point for the red line?Do these lines intersect? If so what is that point? If the lines do not intersect, use no solution in both blanks.What is the rate of change for the red line?What is the rate of the slope of the blue line?What is the y-intercept of the blue line?What is the solution?

Answer 1

(-11, 1)

(-9, -1)

-0.8

1/4

1

(-9, -1)

Step-by-step explanation

- The starting point for the red line is (-11, 1)

- The lines intersect, that is, they touch each other. They intersect at point (-9, -1)

- The rate of change is the same as the slope.

The slope is gotten by picking any two points on the graph and finding:

`\text{Slope = }\frac{y_{2\text{ }}-y_1}{x_{2\text{ }}-x_1}`

Let us pick points (-8, -2) and (-3, -6).

Therefore, the slope for the red line is:

`\text{Slope = }\frac{-6\text{ - (-2)}}{-3-(-8)}\text{ = }\frac{-6\text{ + 2}}{-3\text{ + 8}}=\text{ }(-4)/(5)=\text{ -0.8}`

- For the blue line, let us pick points (-4, 0) and (0, 1)

The slope for the blue line is:

`\text{Slope = }\frac{1\text{ - 0}}{0\text{ - (-4)}}\text{ = }(1)/(4)`

- The y intercept of the blue line is 1

- The solution of the system of lines in the graph is the point of intersection of both lines and that is (-9, -1)