find the slope - intercept form of the line that satisfies the given conditions. through a(9, 4) and b(-7, 6)

Explanation:

Step1: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(9,4)$ and $(x_2,y_2)=(-7,6)$. Then $m=\frac{6 - 4}{-7 - 9}=\frac{2}{-16}=-\frac{1}{8}$.

Step2: Use the point - slope form $y - y_1=m(x - x_1)$

Choose the point $(x_1,y_1)=(9,4)$ and $m =-\frac{1}{8}$. The point - slope form is $y - 4=-\frac{1}{8}(x - 9)$.

Step3: Convert to slope - intercept form $y=mx + b$

Expand the right - hand side: $y-4=-\frac{1}{8}x+\frac{9}{8}$. Then add 4 to both sides: $y=-\frac{1}{8}x+\frac{9}{8}+4$. Since $4=\frac{32}{8}$, we have $y=-\frac{1}{8}x+\frac{9 + 32}{8}=-\frac{1}{8}x+\frac{41}{8}$.

Answer:

$y =-\frac{1}{8}x+\frac{41}{8}$