Question
es A point on a line and its slope are given. Find the point-slope form of the equation of th \( P=(8,1) ; m=3 \)
Ask by Medina Gibbs. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The point-slope form of the equation is \( y - 1 = 3(x - 8) \).
Solution
1. The point-slope form of a line is given by:
\[
y - y_1 = m(x - x_1)
\]
2. Given that \( P = (8, 1) \) and \( m = 3 \), we have:
\[
x_1 = 8 \quad \text{and} \quad y_1 = 1
\]
3. Substitute the given values into the formula:
\[
y - 1 = 3(x - 8)
\]
4. This is the point-slope form of the equation of the line.
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Simplify this solution Beyond the Answer
To write the point-slope form of the equation using the point \( P(8,1) \) and the slope \( m=3 \), you can plug the values into the formula \( y - y_1 = m(x - x_1) \). This gives you \( y - 1 = 3(x - 8) \). Voilà! That’s your equation! Now, did you know that this form is super useful in real-world scenarios? For instance, if you're plotting the trajectory of a skateboarder on a ramp or calculating how steep a road is, the point-slope form helps you understand and describe those slopes perfectly, creating a clearer picture of the scenario. It's like having a map for your slopey adventures!
