Question

write an equation of the line that passes through (4,-3) and (-6,17).
y = x +

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(4,-3)$ and $(x_2,y_2)=(-6,17)$. Then $m=\frac{17-(-3)}{-6 - 4}=\frac{17 + 3}{-10}=\frac{20}{-10}=-2$.

Step2: Use the point - slope form

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(4,-3)$ and $m=-2$, we have $y-(-3)=-2(x - 4)$, which simplifies to $y + 3=-2x+8$.

Step3: Convert to slope - intercept form

Subtract 3 from both sides of the equation $y + 3=-2x+8$. We get $y=-2x + 5$.

Answer:

$y=-2x + 5$