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