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

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

Step2: Find y-intercept using point-slope

Use point $(6,1)$ and $m=-\frac{2}{3}$ in $y=mx+b$.
$1 = -\frac{2}{3}(6) + b$
$1 = -4 + b$
$b=1+4=5$

Step3: Write the line equation

Substitute $m=-\frac{2}{3}$ and $b=5$ into $y=mx+b$.
$y=-\frac{2}{3}x+5$

Step4: Plot the given points

Mark $(9,-1)$ and $(6,1)$ on the coordinate grid, then draw a straight line through them extending in both directions.

Answer:

Equation of the line: $\boldsymbol{y=-\frac{2}{3}x+5}$
(Graph: The line passes through points $(6,1)$ and $(9,-1)$, with a y-intercept at $(0,5)$ and extends infinitely in both directions.)