Question

a line has a slope of 6 and passes through the point (2, 7). 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. We know $m = 6$, so the equation becomes $y=6x + b$.

Step2: Substitute the point values

Substitute $x = 2$ and $y = 7$ into the equation $y = 6x + b$. We get $7=6\times2 + b$.

Step3: Solve for $b$

First, calculate $6\times2=12$. Then the equation is $7 = 12 + b$. Subtract 12 from both sides: $b=7 - 12=-5$.

Step4: Write the final equation

Substitute $b=-5$ back into $y = 6x + b$. The equation of the line is $y = 6x-5$.

Answer:

$y = 6x - 5$