Answer:
y = [tex]\frac{-2}{3}[/tex]x + [tex]\frac{11}{3}[/tex]
Step-by-step explanation:
Step 1: Use the slope formula to determine the slope
We know that the y value decrease by 2 and the x increases by 3 so the formula of [tex]\frac{deltaY}{deltaX}[/tex] can also be written as [tex]\frac{-2}{3}[/tex]
(delta Y and delta X represent the change in the x and y)
Step 2: Find the y-intercept
We substitute the slope and the point(-2, 5) into y=mx+b to solve for b
(5)=([tex]\frac{-2}{3}[/tex])(-2) + b
5 = [tex]\frac{4}{3}[/tex] + b
5 - [tex]\frac{4}{3}[/tex] = b
b = [tex]\frac{11}{3}[/tex]
Step 3: Write the equation out
y = mx+ b
y = [tex]\frac{-2}{3}[/tex]x + [tex]\frac{11}{3}[/tex]
Therefore the equation of a line that passes through the point (-2, 5) with a change in the x value of 3 and y value of -2 is y = [tex]\frac{-2}{3}[/tex]x + [tex]\frac{11}{3}[/tex]
