Question

simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Step1: Identify 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: Assign point values

Let $(x_1,y_1)=(2,2)$ and $(x_2,y_2)=(4,7)$

Step3: Calculate slope

$m=\frac{7-2}{4-2}=\frac{5}{2}$

Step4: Find y-intercept

Use $y=mx+b$, substitute $x=2,y=2,m=\frac{5}{2}$:
$2=\frac{5}{2}(2)+b$
$2=5+b$
$b=2-5=-3$

Step5: Write line equation

$y=\frac{5}{2}x-3$

Answer:

The slope of the line is $\frac{5}{2}$, and the equation of the line is $y=\frac{5}{2}x-3$