Question

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

Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answer 1

`y = x-7`

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`