Question
Write the equation of a line in point-slope form that passes through the point \( (2, 3) \) with a slope of \( 4 \).
Ask by Norris Davies. in India
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The equation of the line in point-slope form is \( y - 3 = 4(x - 2) \).
Solution
To write the equation of a line in **point-slope form**, you can use the following formula:
\[
y - y_1 = m(x - x_1)
\]
where:
- \( (x_1, y_1) \) is a point on the line.
- \( m \) is the slope of the line.
**Given:**
- Point \( (2, 3) \), so \( x_1 = 2 \) and \( y_1 = 3 \).
- Slope \( m = 4 \).
**Plugging these values into the point-slope form:**
\[
y - 3 = 4(x - 2)
\]
**So, the equation of the line is:**
\[
\boxed{y - 3 = 4(x - 2)}
\]
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To write the equation of a line in point-slope form, you can use the formula \( y - y_1 = m(x - x_1) \). Here, \( (x_1, y_1) \) is the point the line passes through, which is \( (2, 3) \), and \( m \) is the slope, which is \( 4 \). Plugging in the values, the equation becomes \( y - 3 = 4(x - 2) \). This equation represents a line that rises steeply, showcasing how the y-value increases by 4 for every 1-unit increase in the x-value. So if you were to draw it, you’d see a line angling up quickly—perfect for those who enjoy dramatic climbs!
