Question

1. find the slope of the line that goes through the points (7, 10) and (9, 8)
2. graph the line y + 3 = 3/4(x - 2)

Explanation:

Step1: Recall slope formula

The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Identify the points

Let $(x_1,y_1)=(7,10)$ and $(x_2,y_2)=(9,8)$.

Step3: Calculate the slope

$m=\frac{8 - 10}{9 - 7}=\frac{-2}{2}=-1$

Step4: Rewrite the line equation in slope - intercept form

Given $y + 3=\frac{3}{4}(x - 2)$, expand the right - hand side: $y+3=\frac{3}{4}x-\frac{3}{2}$. Then isolate $y$: $y=\frac{3}{4}x-\frac{3}{2}-3=\frac{3}{4}x-\frac{3 + 6}{2}=\frac{3}{4}x-\frac{9}{2}$.

Step5: Find the y - intercept

When $x = 0$, $y=\frac{3}{4}(0)-\frac{9}{2}=-\frac{9}{2}=-4.5$.

Step6: Find another point

Let $x = 2$, then $y=\frac{3}{4}(2)-\frac{9}{2}=\frac{3}{2}-\frac{9}{2}=\frac{3 - 9}{2}=-3$.

Answer:

1. The slope of the line is $-1$.
2. To graph the line $y=\frac{3}{4}x-\frac{9}{2}$, plot the y - intercept $(0,-4.5)$ and the point $(2,-3)$ and draw a straight line through them.