Linear Equations in Two Variables

SAT Math · Axiom Academy

Linear Equations in Two Variables Graphing lines and converting between forms This lesson covers the three main forms of linear equations and how to convert between them: Slope-Intercept Form: y = mx + b Point-Slope Form: y - y_1 = m(x - x_1) b = y-intercept (where the line crosses the y-axis) Slope measures how steep a line is: Where A, B, and C are integers and A is non-negative. How to Graph from Standard Form Find the intercepts, then plot and draw the line. Use this form when you know a point (x_1, y_1) and the slope m . Standard Form → Slope-Intercept Form Slope-Intercept Form → Standard Form Point-Slope Form → Slope-Intercept Form Finding the Slope from Two Points Given two points, always use this formula: Slope-Intercept is fastest: If the problem allows, convert to y = mx + b to read m and b directly. Check your work: Pick a point on the line and verify it satisfies the equation. Watch the sign: A negative slope is tricky. The line goes DOWN, not up. Parallel lines: Same slope, different y-intercept. Perpendicular lines: slopes multiply to -1.

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