Algebra 1 Practice - Write an Equation in Point-Slope Form (Example 2)
To write an equation in point-slope form, you can use either two points or a point and a slope. Here’s how to do it for each case:
1. *Using Two Points*
If you have two points \((x_1, y_1)\) and \((x_2, y_2)\), follow these steps:
1. *Calculate the Slope \( m \):*
The slope \( m \) of the line through these two points is given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
2. *Use Point-Slope Form:*
The point-slope form of the line’s equation is:
\[
y - y_1 = m(x - x_1)
\]
Substitute \( m \) (the slope you just calculated) and one of the points \((x_1, y_1)\) into this formula.
*Example:*
Points = (2, 3) and (4, 7)
Calculate the slope \( m \):
\[
m = \frac{7 - 3}{4 - 2} = \frac{4}{2} = 2
\]
Use point (2, 3) and slope 2 in the point-slope form:
\[
y - 3 = 2(x - 2)
\]
2. *Using a Point and a Slope*
If you have a point \((x_1, y_1)\) and a slope \( m \):
1. *Substitute the Slope and the Point:*
Plug the given slope \( m \) and the point \((x_1, y_1)\) into the point-slope form:
\[
y - y_1 = m(x - x_1)
\]
This directly gives you the equation of the line.
*Example:*
Slope (\( m \)) = -3
Point = (5, 2)
Use the point (5, 2) and slope -3 in the point-slope form:
\[
y - 2 = -3(x - 5)
\]
Summary
*Using Two Points:* Calculate the slope \( m \) with the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \), then use \( y - y_1 = m(x - x_1) \) with one of the points.
*Using a Point and a Slope:* Substitute the given slope \( m \) and point \((x_1, y_1)\) into \( y - y_1 = m(x - x_1) \).
This point-slope form provides a straightforward way to represent the equation of a line based on specific points and slopes. #math #shorts #funny #help #onlineclasses #onlinelearning #online #study