Equation from two points
Equation from two points is a Grade 7 math skill from Yoshiwara Intermediate Algebra where students derive the equation of a line given two coordinate pairs. The process involves computing slope from the two points and using point-slope or slope-intercept form to write the full equation.
Key Concepts
Property To find the equation of a line passing through two points, $(x 1, y 1)$ and $(x 2, y 2)$, first calculate the slope using the formula $m = \frac{y 2 y 1}{x 2 x 1}$. Then, use this slope and one of the points with the point slope form, $y y 1 = m(x x 1)$, to write the equation.
Examples Find the equation of the line passing through $(2, 5)$ and $(4, 9)$. First, find the slope: $m = \frac{9 5}{4 2} = \frac{4}{2} = 2$. Using point slope form with $(2, 5)$, we get $y 5 = 2(x 2)$.
What is the equation of the line containing points $( 1, 6)$ and $(3, 2)$? The slope is $m = \frac{ 2 6}{3 ( 1)} = \frac{ 8}{4} = 2$. Using point $( 1, 6)$, the equation is $y 6 = 2(x + 1)$.
Common Questions
How do you find the equation of a line from two points?
Calculate slope m = (y2-y1)/(x2-x1), then use one point in y - y1 = m(x - x1) and simplify to y = mx + b form.
How do you find the equation through (2, 1) and (5, 7)?
m = (7-1)/(5-2) = 2. Using point (2,1): y - 1 = 2(x - 2), so y = 2x - 3.
Do you always get the same equation regardless of which point you use?
Yes. Both points lie on the same line, so using either point in the point-slope form produces the same final equation.
What if the two points have the same x-coordinate?
If x1 = x2, the line is vertical with equation x = x1. Its slope is undefined.