Answer:
(8, -22)
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
First table:
(-4, 26), (0, 10) → b = 10
[tex]m=\dfrac{10-26}{0-(-4)}=\dfrac{-16}{4}=-4[/tex]
[tex]\boxed{y=-4x+10}[/tex]
Second table:
(-4, 14), (0, 2) → b = 2
[tex]m=\dfrac{2-14}{0-(-4)}=\dfrac{-12}{4}=-3[/tex]
[tex]\boxed{y=-3x+2}[/tex]
We have the system of equations:
[tex]\left\{\begin{array}{ccc}y=-4x+10&(1)\\y=-3x+2&(2)\end{array}\right\\\\\text{Put (1) to (2):}\\\\-4x+10=-3x+2\qquad\text{subtract 10 from both sides}\\-4x=-3x-8\qquad\text{add 3x to both sides}\\-x=-8\qquad\text{change the signs}\\x=8\\\\\text{Put the value of x to (2):}\\\\y=-3(8)+2\\y=-24+2\\y=-22[/tex]
