Question

A line has a slope of -3/7 and passes through the point (5,-1). What is the equation of the line in slope-intercept form?

Answer 1

To find the equation of a line in slope-intercept form \(y = mx + b\), we need to use the given slope and a point on the line.

We are given:
- Slope (\(m\)) = \(-\frac{3}{7}\)
- Point = \((5, -1)\)

We can start by using the point to find the y-intercept (\(b\)). The slope-intercept form of the line is:

\[
y = mx + b
\]

Substituting the values we have:

\[
-1 = -\frac{3}{7}(5) + b
\]

Calculating \(-\frac{3}{7}(5)\):

\[
-\frac{3}{7} \times 5 = -\frac{15}{7}
\]

Now, substitute this back into the equation:

\[
-1 = -\frac{15}{7} + b
\]

Next, to isolate \(b\), we need to add \(-\frac{15}{7}\) to both sides:

\[
b = -1 + \frac{15}{7}
\]

To perform this addition, we need to convert \(-1\) into a fraction with a denominator of 7:

\[
-1 = -\frac{7}{7}
\]

Now we can combine the fractions:

\[
b = -\frac{7}{7} + \frac{15}{7} = \frac{-7 + 15}{7} = \frac{8}{7}
\]

Now we have both the slope and the y-intercept:

- Slope \(m = -\frac{3}{7}\)
- Y-intercept \(b = \frac{8}{7}\)

The equation of the line in slope-intercept form is:

\[
y = -\frac{3}{7}x + \frac{8}{7}
\]

Thus, the final answer is:

\[
\boxed{y = -\frac{3}{7}x + \frac{8}{7}}
\]