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Solve for y

Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 20 of 64.

An equation is not always given in slope-intercept form. The equation 2x + 3y = 6 describes a line, so it can be written as y = mx + b. To find that form, solve the equation for y, then divide each term:

2x + 3y = 6

3y = -2x + 6

y = (-2x + 6)/3

y = -2/3x + 2

Now you can read the slope, -2/3, and the y-intercept, (0, 2). The last step splits the fraction into two terms. Without it, the answer is correct, but you cannot read m and b from it.

For a nonvertical line, isolate y and simplify the right side to mx + b. The coefficient of x is the slope m, and the constant term is the y-intercept b.

Challenge

Medium

Rewrite 3x + 2y = 8 in slope-intercept form. Solve for y, then multiply everything out.

Try it yourself

3x + 2y = 8

Solve for y

Test yourself

This 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 Point The Four Quadrants Points on the Axes Mirror Points Recap: The Plane

4Slope-Intercept Form

y = mx + b The Starting Height Write the EquationSolve for yDraw From Any Form Recap: y = mx + b

7Parallel & Perpendicular

Same Slope, Never Meet The Perpendicular Slope A Right-Angle Line Recap: Two Relations

10Systems by Graphing

Two Lines, One Answer Solve by Drawing Check the Crossing When Lines Never Cross Recap: By Graphing

2From Rule to Line

A Rule Makes Points The Points Line Up On the Line or Not?Between the Dots Recap: Rule to Line

5Point-Slope Form

A Point and a Slope From Two Points Flat or Vertical Through Draw From a Point Recap: Point-Slope

8Function Notation

The Name of a Rule Inputs With Signs Find the Input The Graph of f Recap: f(x)

11Solving Systems Exactly

Substitution Isolate First Elimination Scale, Then Add Three Unknowns Two Numbers, Two Facts Recap: Two Methods