Martinez Smith
01/09/2024 · Primary School
A line passes through the point \( (-8,-9) \) and has a slope of \( \frac{5}{4} \). Write an equation in slope-intercept form for this line.
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Tutor-Verified Answer
Step-by-step Solution
To write the equation of a line in slope-intercept form, we use the formula:
\[
y = mx + b
\]
where \( m \) is the slope and \( b \) is the y-intercept. We are given the slope \( m = \frac{5}{4} \) and a point on the line \( (-8, -9) \).
First, we can substitute the slope and the coordinates of the point into the equation to find \( b \):
\[
-9 = \frac{5}{4}(-8) + b
\]
Calculating \( \frac{5}{4}(-8) \):
\[
\frac{5}{4} \times -8 = -10
\]
Now substitute this back into the equation:
\[
-9 = -10 + b
\]
To solve for \( b \), add 10 to both sides:
\[
-9 + 10 = b
\]
\[
b = 1
\]
Now that we have the slope \( m = \frac{5}{4} \) and the y-intercept \( b = 1 \), we can write the equation of the line in slope-intercept form:
\[
y = \frac{5}{4}x + 1
\]
Thus, the equation of the line is:
\[
\boxed{y = \frac{5}{4}x + 1}
\]
Quick Answer
The equation of the line is \( y = \frac{5}{4}x + 1 \).
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