Writing an Equation from Any Two Points
Writing an equation from any two points in Algebra 1 (California Reveal Math, Grade 9) requires two steps: (1) calculate the slope using m = (y₂ - y₁)/(x₂ - x₁), then (2) substitute the slope and one point into y = mx + b and solve for b. For example, from (1, 3) and (3, 7): m = (7-3)/(3-1) = 2, then 3 = 2(1) + b → b = 1, giving y = 2x + 1. This procedure works for any two non-identical points and is fundamental for modeling real-world linear relationships from data.
Key Concepts
To write an equation in slope intercept form $y = mx + b$ from any two points:.
1. Calculate the slope using $$m = \frac{y 2 y 1}{x 2 x 1}$$ 2. Substitute $m$ and one point $(x, y)$ into $y = mx + b$ and solve for $b$ 3. Write the final equation using the values of $m$ and $b$.
Common Questions
How do you write a linear equation from two points?
Step 1: Calculate slope: m = (y₂ - y₁)/(x₂ - x₁). Step 2: Substitute m and one point into y = mx + b, then solve for b.
Can you show a full example?
Points (2, 5) and (4, 9): m = (9-5)/(4-2) = 2. Using (2, 5): 5 = 2(2) + b → b = 1. Equation: y = 2x + 1.
What if you want to use point-slope form instead of slope-intercept?
You can write y - y₁ = m(x - x₁) directly without finding b. For m = 2 and point (2, 5): y - 5 = 2(x - 2). Both forms are correct.
What is the slope formula?
m = (y₂ - y₁)/(x₂ - x₁). It measures the change in y (rise) divided by the change in x (run) between two points.
Where is writing equations from two points covered in California Reveal Math Algebra 1?
This skill is taught in California Reveal Math, Algebra 1, as part of Grade 9 linear functions and equations.
What if the slope is undefined (vertical line)?
A vertical line has undefined slope — the two points have the same x-coordinate. Its equation is x = c (a constant), not a function.
Why do you need two points instead of just one to write a unique line equation?
One point is satisfied by infinitely many lines of different slopes. Two distinct points determine exactly one line, giving a unique equation.