Question

graph the line that passes through the points (9, -1) and (6, 1) and determine the equation of the line.

Explanation:

Step1: Calculate slope of the line

The slope formula is $m=\frac{y_2-y_1}{x_2-x_1}$. Let $(x_1,y_1)=(9,-1)$ and $(x_2,y_2)=(6,1)$.
$m=\frac{1-(-1)}{6-9}=\frac{2}{-3}=-\frac{2}{3}$

Step2: Find y-intercept using point-slope form

Use point-slope form $y-y_1=m(x-x_1)$ with $(x_1,y_1)=(6,1)$:
$y-1=-\frac{2}{3}(x-6)$
Simplify to slope-intercept form $y=mx+b$:
$y-1=-\frac{2}{3}x + 4$
$y=-\frac{2}{3}x + 5$

Step3: Verify with the second point

Substitute $(9,-1)$ into $y=-\frac{2}{3}x + 5$:
$y=-\frac{2}{3}(9)+5=-6+5=-1$, which matches the point.

Answer:

The equation of the line is $\boldsymbol{y=-\frac{2}{3}x + 5}$. To graph it: plot the points $(9,-1)$ and $(6,1)$, then draw a straight line passing through both points, which will cross the y-axis at $(0,5)$.