A Point and a Slope
Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 23 of 64.
A slope and one point, any point, also pin a line down, and there is a form built for exactly that data. A line through (x1, y1) with slope m satisfies
y - y1 = m(x - x1)
the point-slope form. Through (1, 2) with slope 3 it reads y - 2 = 3(x - 1), and expanding turns it into slope-intercept: y - 2 = 3x - 3, so y = 3x - 1.
The form is just the slope formula rearranged: any (x, y) on the line makes rise over run equal m, and multiplying by the run gives the equation. Plug in the known point, expand, done.
Challenge
A line through (1, 2) with slope 3 satisfies y - 2 = 3(x - 1). Rewrite it in slope-intercept form: solve for y and multiply everything out.
Try it yourself
Solve for y
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Graphs & Systems
1The Coordinate Plane
Two Numbers, One PointThe Four QuadrantsPoints on the AxesMirror PointsRecap: The Plane4Slope-Intercept Form
y = mx + bThe Starting HeightWrite the EquationSolve for yDraw From Any FormRecap: y = mx + b7Parallel & Perpendicular
Same Slope, Never MeetThe Perpendicular SlopeA Right-Angle LineRecap: Two Relations2From Rule to Line
A Rule Makes PointsThe Points Line UpOn the Line or Not?Between the DotsRecap: Rule to Line5Point-Slope Form
A Point and a SlopeFrom Two PointsFlat or Vertical ThroughDraw From a PointRecap: Point-Slope