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Lesson 12 Name: Writing a Linear Equation in Slope-Intercept Form Study the example problem showing how to write an equation in slope-intercept form. Then solve problems 1â6. Example y Write an equation for the line shown in the diagram. 8 7 6 Find the slope of the line. y 2 y1 7 2 3 Use the slope formula. â¯ââ¯ â¯ 5 ââ¯ â¯â¯ â â¯ m 5 ââ¯ 2 x2 2 x1 Â·Â·Â·Â·Â· 2 2 0 Substitute 7 for y2, 3 for Â·Â·Â·Â·Â·Â· y1, 2 for x2, and 0 for x1. m 5 ââ¯4â¯â, or 2 2 Â·Â· Simplify. The slope is 2. 5 4 3 1 22 21 O 1 2 3 4 5 x 6 The line passes through (0, 3), so the y-intercept is 3. Use the slope-intercept form y 5 mx 1 b to write an equation. y 5 mx 1 b y 5 2x 1 3 Substitute 2 for m and 3 for b. An equation for the line is y 5 2x 1 3. 1 How is the equation y 5 2x similar to the equation y 5 2x 1 3 in the example problem? How is it different? 2 Graph y 5 2x in the diagram above. Compare the graphs. Does either graph represent a proportional relationship? Explain. Vocabulary slopeâ the ratio of the vertical change (rise) to the horizontal change (run) between any two points on a line. y-interceptâ the y-coordinate of the point where a graph intersects the y-axis. y 7 6 5 4 2 1 3 What value of b makes y 5 2x 1 b the same as y 5 2x? What does that value mean? Â©Curriculum Associates, LLCâ Copying is not permitted. (0, 3) 21 O 21 1 2 3 4 6 7 x The y-intercept is 3. Lesson 12â Understand the Slope-Intercept Equation for a Line 135