Question

a line passes through the points (1, 1) and (2, 8). 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 $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Given $(x_1,y_1)=(1,1)$ and $(x_2,y_2)=(2,8)$, then $m=\frac{8 - 1}{2 - 1}=\frac{7}{1}=7$.

Step2: Find the y - intercept

The slope - intercept form is $y=mx + b$. Substitute $m = 7$, $x = 1$ and $y = 1$ into the equation: $1=7\times1 + b$. Solve for $b$: $b=1 - 7=-6$.

Step3: Write the equation

The equation of the line in slope - intercept form is $y = mx + b$. Substitute $m = 7$ and $b=-6$ to get $y=7x - 6$.

Answer:

$y = 7x-6$