Question
A line has a slope of -3 and passes through the point \( (4,-15) \). Write its equation in slope- intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form.
Ask by Schofield Adkins. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The equation of the line in slope-intercept form is \( y = -3x - 3 \).
Solution
The slope-intercept form of a line is given by:
\[
y = mx + b
\]
where \( m \) is the slope and \( b \) is the y-intercept.
Given:
- Slope (\( m \)) = -3
- The line passes through the point \( (4, -15) \).
First, substitute the slope and the coordinates of the point into the equation to solve for \( b \):
\[
-15 = (-3)(4) + b
\]
\[
-15 = -12 + b
\]
\[
b = -15 + 12
\]
\[
b = -3
\]
So, the equation of the line in slope-intercept form is:
\[
y = -3x - 3
\]
**Answer:**
\( y = -3x - 3 \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To find the equation of the line in slope-intercept form \( y = mx + b \), we start with the given slope \( m = -3 \) and the point \( (4, -15) \). We can substitute these values into the equation to find \( b \): \[ -15 = -3(4) + b \] \[ -15 = -12 + b \] \[ b = -15 + 12 = -3 \] Now we can write the equation of the line: \[ y = -3x - 3 \] So, the equation in slope-intercept form is \( y = -3x - 3 \).
