Point-Slope Form
Point-slope form is a Grade 7 math skill from Yoshiwara Intermediate Algebra used to write the equation of a line given a point and a slope. The form y - y1 = m(x - x1) is especially useful when the y-intercept is not given directly.
Key Concepts
Property The point slope form of a linear equation is $y = y 1 + m(x x 1)$, where $m$ is the slope and $(x 1, y 1)$ is any known point on the line.
This form is useful for finding the equation of a line when you know its slope and at least one point it passes through.
You may also see the formula written in an alternate version: $$y y 1=m(x x 1) \quad \text{or} \quad \frac{y y 1}{x x 1}=m$$.
Common Questions
What is point-slope form?
Point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a specific point on the line.
How do you use point-slope form?
Substitute the known slope and point into y - y1 = m(x - x1). You can leave it in this form or simplify to slope-intercept form y = mx + b.
How do you find the equation of a line with slope 3 through (2, 5)?
Substitute into point-slope form: y - 5 = 3(x - 2). Simplified: y = 3x - 1.
When is point-slope form more useful than slope-intercept form?
Point-slope form is more useful when you know the slope and a non-intercept point, avoiding the extra step of finding b.