Question

Caleb graphed the linear function y = –x + 2 of a system of equations. The other linear function passes through the points (–2, –8) and (1, –2). What is the slope of the linear function that passes through the points (–2, –8) and (1, –2)? What is the y-intercept? Graph the linear function to determine the solution. What is the solution?

Answer 1

Answer:

its

2

-4

(2,0)

i took the test and got it right

Step-by-step explanation:

Answer 2

Answer:

Part 1) $m=2$

Part 2) The y-intercept is the point (0,-4)

Part 3) The solution of the system is (2,0) (the graph in the attached figure)

Step-by-step explanation:

Part 1) What is the slope of the linear function that passes through the points (–2, –8) and (1, –2)?

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{-2+8}{1+2}$

$m=\frac{6}{3}$

$m=2$

Part 2) What is the y-intercept?

Find the equation of the line in slope intercept form

$y=mx+b$

we have

$m=2$

$point\ (1,-2)$

substitute and solve for b

$-2=2(1)+b\\b=-4$

so

$y=2x-4$

The y-intercept is the point (0,-4)

Part 3) Graph the linear function to determine the solution. What is the solution?

we have

$y=-x+2$ ----> equation A

$y=2x-4$ ----> equation B

Solve the system by graphing

The solution is the intersection point both graphs

using a graphing tool

The solution of the system is (2,0)

see the attached figure