Question

A line has a slope of
2
7
and passes through the point (7,0). Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answer 1

To find the equation of a line in slope-intercept form, we need to use the slope-intercept formula, which is:

\[
y = mx + b
\]

where \( m \) is the slope and \( b \) is the y-intercept.

Given that the slope \( m \) is \( \frac{2}{7} \) and the line passes through the point \( (7, 0) \), we can find the y-intercept \( b \) by substituting \( x = 7 \) and \( y = 0 \) into the equation and solving for \( b \).

Substituting into the equation:

\[
0 = \frac{2}{7}(7) + b
\]

Simplifying:

\[
0 = 2 + b
\]

Solving for \( b \):

\[
b = -2
\]

Now we can write the equation in slope-intercept form using the slope \( m = \frac{2}{7} \) and the y-intercept \( b = -2 \):

\[
y = \frac{2}{7}x - 2
\]

Thus, the equation of the line in slope-intercept form is:

\[
y = \frac{2}{7}x - 2
\]