Science, Tech, Math › Math What Slope-Intercept Form Means and How to Find It Share Flipboard Email Print Math Pre Algebra & Algebra Math Tutorials Geometry Arithmetic Statistics Exponential Decay Functions Worksheets By Grade Resources View More By Jennifer Ledwith Math Expert B.B.A., Finance and Economics, University of Oklahoma Jennifer Ledwith is the owner of tutoring and test-preparation company Scholar Ready, LLC and a professional writer, covering math-related topics. our editorial process Jennifer Ledwith Updated March 04, 2019 The slope-intercept form of an equation is y = mx + b, which defines a line. When the line is graphed, m is the slope of the line and b is where the line crosses the y-axis or the y-intercept. You can use slope intercept form to solve for x, y, m, and b. Follow along with these examples to see how to translate linear functions into a graph-friendly format, slope intercept form and how to solve for algebra variables using this type of equation. 01 of 03 Two Formats of Linear Functions commerceandculturestock Standard Form: ax + by = c Examples: 5x + 3y = 18-¾x + 4y = 029 = x + y Slope intercept form: y = mx + b Examples: y = 18 - 5xy = x¼x + 3 = y The primary difference between these two forms is y. In slope-intercept form — unlike standard form —y is isolated. If you're interested in graphing a linear function on paper or with a graphing calculator, you'll quickly learn that an isolated y contributes to a frustration-free math experience. Slope intercept form gets straight to the point: y = mx + b m represents the slope of a lineb represents the y-intercept of a linex and y represent the ordered pairs throughout a line Learn how to solve for y in linear equations with single and multiple step solving. 02 of 03 Single Step Solving Example 1: One Step Solve for y, when x + y = 10. 1. Subtract x from both sides of the equal sign. x + y - x = 10 - x0 + y = 10 - xy = 10 - x Note: 10 - x is not 9x. (Why? Review Combining Like Terms.) Example 2: One Step Write the following equation in slope intercept form: -5x + y = 16 In other words, solve for y. 1. Add 5x to both sides of the equal sign. -5x + y + 5x = 16 + 5x0 + y = 16 + 5xy = 16 + 5x 03 of 03 Multiple Step Solving Example 3: Multiple Steps Solve for y, when ½x + -y = 12 1. Rewrite -y as + -1y. ½x + -1y = 12 2. Subtract ½x from both sides of the equal sign. ½x + -1y - ½x = 12 - ½x0 + -1y = 12 - ½x-1y = 12 - ½x-1y = 12 + - ½x 3. Divide everything by -1. -1y/-1 = 12/-1 + - ½x/-1y = -12 + ½x Example 4: Multiple Steps Solve for y when 8x + 5y = 40. 1. Subtract 8x from both sides of the equal sign. 8x + 5y - 8x = 40 - 8x0 + 5y = 40 - 8x5y = 40 - 8x 2. Rewrite -8x as + - 8x. 5y = 40 + - 8x Hint: This is a proactive step toward correct signs. (Positive terms are positive; negative terms, negative.) 3. Divide everything by 5. 5y/5 = 40/5 + - 8x/5y = 8 + -8x/5 Edited by Anne Marie Helmenstine, Ph.D.