Question
A line has a slope of 7 and passes through the point \( (-1,-8) \). Write its equation in slope- intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form.
Ask by Turnbull Long. in the United States
Jan 15,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The equation of the line is \( y = 7x - 1 \).
Solution
To find the equation of a line with a slope of 7 that passes through the point \((-1, -8)\), we can use the **slope-intercept form** of a line, which is:
\[
y = mx + b
\]
where:
- \( m \) is the slope
- \( b \) is the y-intercept
Given:
- Slope (\( m \)) = 7
- Point \((-1, -8)\) lies on the line
Plugging the known values into the equation:
\[
-8 = 7(-1) + b
\]
\[
-8 = -7 + b
\]
Solving for \( b \):
\[
b = -8 + 7
\]
\[
b = -1
\]
Now, substitute \( m \) and \( b \) back into the slope-intercept form:
\[
y = 7x - 1
\]
**Final Answer:**
\[
y = 7x - 1
\]
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Simplify this solution Bonus Knowledge
To find the equation of the line in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, we start with the slope, which is given as 7. We can use the point \( (-1, -8) \) to find \( b \). Using the point to substitute: \[ -8 = 7(-1) + b \] This simplifies to: \[ -8 = -7 + b \] Now, solving for \( b \): \[ b = -8 + 7 = -1 \] Therefore, the equation of the line in slope-intercept form is: \[ y = 7x - 1 \] It’s all set with integers ready to roll!
