Reese Lowe
07/24/2023 · Junior High School
A line passes through the point \( (5,-8) \) and has a slope of 2 . Write an equation in slope-intercept form for this line.
UpStudy ThothAI Solution
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.
Given that the slope \( m = 2 \) and the line passes through the point \( (5, -8) \), we can substitute these values into the equation to find \( b \).
First, substitute \( x = 5 \), \( y = -8 \), and \( m = 2 \) into the equation:
\[
-8 = 2(5) + b
\]
Now, calculate \( 2(5) \):
\[
-8 = 10 + b
\]
Next, solve for \( b \) by subtracting 10 from both sides:
\[
-8 - 10 = b
\]
\[
b = -18
\]
Now that we have the slope \( m = 2 \) and the y-intercept \( b = -18 \), we can write the equation of the line in slope-intercept form:
\[
y = 2x - 18
\]
Thus, the equation of the line is:
\[
\boxed{y = 2x - 18}
\]
Quick Answer
The equation of the line is \( y = 2x - 18 \).
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Submit