Question

a line passes through the points (1, 1) and (2, 7). write its equation in slope - intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Calculate the slope

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

Step2: Find y-intercept $b$

Use slope-intercept form $y=mx+b$, substitute $m=6$ and $(x,y)=(1,1)$:
$1=6(1)+b$
Solve for $b$:
$b=1-6=-5$

Step3: Write final equation

Substitute $m=6$ and $b=-5$ into $y=mx+b$.

Answer:

$y=6x-5$