Horton Burgess
07/18/2024 · Junior High School
questions you held earller. Please submit an answer or pass. equation of a line that goes through the point \( (0,-5) \) and has a slope of \( -3 ? \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To find the equation of a line that goes through the point \( (0, -5) \) with a slope of \( -3 \), we can use the point-slope form of the equation of a line, which is given by:
\[
y - y_1 = m(x - x_1)
\]
where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope.
In this case, the point is \( (0, -5) \) (so \( x_1 = 0 \) and \( y_1 = -5 \)), and the slope \( m = -3 \). Plugging these values into the point-slope form gives:
\[
y - (-5) = -3(x - 0)
\]
This simplifies to:
\[
y + 5 = -3x
\]
Now, we can isolate \( y \) to put the equation in slope-intercept form \( y = mx + b \):
\[
y = -3x - 5
\]
Thus, the equation of the line is:
\[
y = -3x - 5
\]
Quick Answer
The equation of the line is \( y = -3x - 5 \).
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