a line passes through the points (6, 7) and (8, 8). write its equation in slope - intercept form. write your…

Explanation:

Step1: Calculate the slope

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

Step2: Use point - slope form to find y - intercept

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(6,7)$ and $m = \frac{1}{2}$, we have $y-7=\frac{1}{2}(x - 6)$. Expand it: $y-7=\frac{1}{2}x-3$.

Step3: Convert to slope - intercept form

Add 7 to both sides of the equation $y-7=\frac{1}{2}x - 3$. We get $y=\frac{1}{2}x+4$.

Answer:

$y=\frac{1}{2}x + 4$