Question

what is an equation of the line that passes through the points (3, - 4) and (- 4, 3)?

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(3,-4)$ and $(x_2,y_2)=(-4,3)$. Then $m=\frac{3-(-4)}{-4 - 3}=\frac{3 + 4}{-7}=\frac{7}{-7}=-1$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(3,-4)$ and $m=-1$, we have $y-(-4)=-1(x - 3)$.

Step3: Simplify the equation

$y + 4=-x + 3$, which simplifies to $y=-x-1$.

Answer:

$y=-x - 1$