Question

A line that includes the point (7,0) has a slope of 1. What is its equation in slope-intercept form?

Answer 1

Answer:

$y = x-7$    

Step-by-step explanation:

To write the equation of the line in slope-intercept form, use the slope-intercept formula, $y = mx +b$. Find real values for the $m$ and $b$ and substitute them into the formula.  

1) We know that $m$ represents the slope, so substitute 1 in its place.  However, we still need to find $b$, or the y-intercept. So, along with substituting that 1 in for $m$, substitute the x and y values for (7,0) for the x and y in the formula as well. Then, isolate $b$ to find its value:

$y = mx + b\\0 = (1)(7)+b\\0 = 7 + b\\-7 = b$

So, $b$ = -7.  

2) Now, just substitute the found values for $m$ and $b$ into the slope-intercept formula. Remember that the slope is $m$, so substitute 1 in, and $b$ is -7, so substitute -7 in its place as well. This gives the following equation in slope-intercept form:

$y = 1x -7$ or $y = x-7$