Equation from two points
Write a linear equation from two points in Grade 10 algebra. Calculate slope using the slope formula, then apply point-slope form to derive the equation in slope-intercept form.
Key Concepts
Given two points, first find the slope with $m = \frac{y 2 y 1}{x 2 x 1}$. Then, use the point slope form $y y 1 = m(x x 1)$ with either point to find the final equation.
Given points $(2, 3)$ and $(4, 7)$. Step 1 (Slope): $m = \frac{7 3}{4 2} = \frac{4}{2} = 2$. Step 2 (Point Slope): $y 3 = 2(x 2)$, which simplifies to $y = 2x 1$. Given $(1000, 5000)$ and $(3000, 0)$. Slope: $m = \frac{0 ( 5000)}{3000 1000} = 2.5$. Equation: $y 0 = 2.5(x 3000)$, so $y = 2.5x 7500$.
You can build the entire equation of a line with just two lonely points! First, find the 'rise over run' to get your slope. Then, grab that slope and one of the points, plug them into the point slope form, and you've built the whole line from scratch.
Common Questions
How do you find the equation of a line from two points?
First calculate slope: m = (y₂ - y₁)/(x₂ - x₁). Then use point-slope form y - y₁ = m(x - x₁) with either point. Simplify to slope-intercept form y = mx + b.
What is point-slope form and why is it useful?
Point-slope form y - y₁ = m(x - x₁) lets you write a line equation directly from a point (x₁, y₁) and slope m without first finding the y-intercept.
How do you find a line equation from two points (1, 3) and (4, 9)?
Slope: m = (9-3)/(4-1) = 6/3 = 2. Using point (1, 3): y - 3 = 2(x - 1) → y = 2x + 1.