Question

A line has a slope of
–
2
5
and passes through the point (17,
–
6). Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answer 1

To write the equation of a line in slope-intercept form, which is given by the equation \( y = mx + b \), we need the slope (\( m \)) and the y-intercept (\( b \)).

Here, the slope \( m = -\frac{2}{5} \) and the line passes through the point \( (17, -6) \).

We can use the point-slope form of the equation of a line:

\[
y - y_1 = m(x - x_1)
\]

Substituting \( m = -\frac{2}{5} \), \( x_1 = 17 \), and \( y_1 = -6 \):

\[
y - (-6) = -\frac{2}{5}(x - 17)
\]

This simplifies to:

\[
y + 6 = -\frac{2}{5}(x - 17)
\]

Now, distribute the slope on the right side:

\[
y + 6 = -\frac{2}{5}x + \frac{34}{5}
\]

Next, we isolate \( y \) by subtracting 6 from both sides. Note that \( 6 \) can be written as \( \frac{30}{5} \):

\[
y = -\frac{2}{5}x + \frac{34}{5} - \frac{30}{5}
\]

Combining the fractions gives:

\[
y = -\frac{2}{5}x + \frac{4}{5}
\]

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

\[
y = -\frac{2}{5}x + \frac{4}{5}
\]