Rewriting an equation in

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Presentation transcript:

Rewriting an equation in Slope-Intercept form

In an equation written in slope-intercept form, y = mx + b, m is the slope and b is the y-intercept.

For an equation such as y = x – 6, write it as y = x + (–6) to read the y-intercept, –6. Helpful Hint

Additional Example 2A: Using Slope-Intercept Form to Find Slopes and y-intercepts Write each equation in slope-intercept form, and then find the slope and y-intercept. A. 2x + y = 3 2x + y = 3 –2x –2x Subtract 2x from both sides. y = 3 – 2x Rewrite to match slope-intercept form. y = –2x + 3 The equation is in slope-intercept form. m = –2 b = 3 The slope of the line 2x + y = 3 is –2, and the y-intercept is 3.

Additional Example 2B: Using Slope-Intercept Form to Find Slopes and y-intercepts B. 5y = 3x 5y = 3x = x 3 5 5y Divide both sides by 5 to solve for y. y = x + 0 3 5 The equation is in slope-intercept form. m = 3 5 b = 0 The slope of the line 5y = 3x is , and the y-intercept is 0. 3 5

Additional Example 2C: Using Slope-Intercept Form to Find Slopes and y-intercepts C. 4x + 3y = 9 4x + 3y = 9 –4x –4x Subtract 4x from both sides. 3y = 9 – 4x Rewrite to match slope-intercept form. 3y = –4x + 9 = + –4x 3 3y 9 Divide both sides by 3. y =- x + 3 4 3 The equation is in slope-intercept form. The slope of the line 4x+ 3y = 9 is – , and the y-intercept is 3. 4 3 m =- 4 3 b = 3

Try This: Example 2A Write each equation in slope-intercept form, and then find the slope and y-intercept. A. 4x + y = 4 –4x –4x Subtract 4x from both sides. y = 4 – 4x Rewrite to match slope-intercept form. y = –4x + 4 The equation is in slope-intercept form. m = –4 b = 4 The slope of the line 4x + y = 4 is –4, and the y-intercept is 4.

Try This: Example 2B B. 7y = 2x 7y = 2x = x 2 7 7y Divide both sides by 7 to solve for y. y = x + 0 2 7 The equation is in slope-intercept form. m = 2 7 b = 0 The slope of the line 7y = 2x is , and the y-intercept is 0. 2 7

Try This: Example 2C C. 5x + 4y = 8 5x + 4y = 8 –5x –5x Subtract 5x from both sides. 4y = 8 – 5x Rewrite to match slope-intercept form. 5x + 4y = 8 = + –5x 4 4y 8 Divide both sides by 4. y =- x + 2 5 4 The equation is in slope-intercept form. The slope of the line 5x + 4y = 8 is – , and the y-intercept is 2. 5 4 m =- 5 4 b = 2