A Point and a Slope
Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 23 of 64.
A line is fixed by one point on it and its slope. Point-slope form writes the equation of the line through the point (x1, y1) with slope m:
y - y1 = m(x - x1)
For the line through (1, 2) with slope 3, substitute the point and the slope: y - 2 = 3(x - 1). To change it into slope-intercept form, expand the bracket to get y - 2 = 3x - 3. Then add 2 to both sides to get y = 3x - 1.
Point-slope form comes from the slope formula. Take any point (x, y) on the line. The rise from (x1, y1) to (x, y) is y - y1 and the run is x - x1, so (y - y1)/(x - x1) = m. Multiply both sides by the run x - x1 to get y - y1 = m(x - x1). To use the form, substitute the known point and the slope, then expand the bracket.
Challenge
MediumRewrite y - 4 = 2(x - 3) in slope-intercept form.
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