Write the Equation
Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 19 of 64.
Slope-intercept form also runs backwards: from a slope and a crossing height, the equation writes itself. A line with slope -2 through (0, 5) must be
y = -2x + 5
because m is the slope and b the crossing height, with nothing else to decide. Watch the signs travel: slope -2 and intercept (0, -3) give y = -2x - 3, the minus of the intercept living inside the b.
This is the first taste of a theme that fills the chapter: a line can be handed over as a picture, a table, a story or an equation, and each form converts into the others.
Challenge
A line has slope 4 and y-intercept (0, -3). Write its equation.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
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 Line