Question

Which system of equations could be used to solve for the point of intersection of the lines on the graph?

Answer 1

Answer:

$y=\frac{3}{4}-1$  and   $y=-\frac{4}{3}+9$

Step-by-step explanation:

step 1

Find the equation of the blue line

take the points

(0,-1) and (8,5) from the graph

Find the slope

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

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

substitute

$m=\frac{5+1}{8-0}$

$m=\frac{6}{8}$

simplify

$m=\frac{3}{4}$

Find the equation of the line in slope intercept form

$y=mx+b$

we have

$m=\frac{3}{4}$

$b=-1$ ---> see the graph

substitute the given values

$y=\frac{3}{4}-1$

step 2

Find the equation of the black line

take the points

(0,9) and (3,5) from the graph

Find the slope

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

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

substitute

$m=\frac{5-9}{3-0}$

$m=-\frac{4}{3}$

Find the equation of the line in slope intercept form

$y=mx+b$

we have

$m=-\frac{4}{3}$

$b=9$ ---> see the graph

substitute the given values

$y=-\frac{4}{3}+9$

therefore

The system of equations is

$y=\frac{3}{4}-1$  and   $y=-\frac{4}{3}+9$