Question

a line has a slope of 7 and passes through the point (2, 8). write its equation in slope - intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Given $m = 7$, the equation becomes $y=7x + b$.

Step2: Substitute the point into the equation

Substitute the point $(x = 2,y = 8)$ into $y = 7x + b$. So, $8=7\times2 + b$.

Step3: Solve for $b$

First, calculate $7\times2=14$. Then the equation $8 = 14 + b$ can be solved for $b$ by subtracting 14 from both sides. $b=8 - 14=- 6$.

Step4: Write the final equation

Substitute $b=-6$ back into $y = 7x + b$. The equation of the line is $y = 7x-6$.

Answer:

$y = 7x-6$