Writing the Equation of a Line

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Writing the Equation of a Line Section 3.4 Writing the Equation of a Line

To Find an Equation of a Line 1. Write the slope-intercept form of the equation of a line: y = mx + b. 2. Find m (if not given). 3. Substitute the given values of x, y, and m into the equation. 4. Solve for b. 5. Use the values of b and m to write the equation in the form y = mx + b.

Example Find an equation of the line that passes through (4, 3) with a slope of 5. m = 5, x = 4, y = 3 y = mx + b 3 = (5)(4) + b 23 = b The equation of the line is y = 5x  23.

Example Find an equation of the line that passes through (2, 1) and (7, 4). Find the slope of the line. y = mx + b The equation of the line is

Example Find the equation of the line for the following graph. Find the y-intercept. Find the slope. x y 1 2 3 4 1 2 3 4 (0, 2) Change in y = 2 (3, 0) Change in x = 3 The equation of the line is

Parallel Lines Parallel lines are two straight lines that never touch. Parallel lines have the same slope but different y-intercepts. x y Slope m1 m1 = m2 Slope m2

Perpendicular Lines Perpendicular lines are two lines that meet in a 90° angle. Perpendicular lines have slopes whose product is –1. If m1 and m2 are slope of perpendicular lines, then m1m2 =  1 x y Slope m2 m1 = Slope m1

Example Line c has a slope of 1/2. If line d is parallel to line c, what is its slope? Parallel lines have the same slope. Line d has a slope of 1/2.

Example Line c has a slope of 1/2. If line e is perpendicular to line c, what is its slope? Perpendicular lines have slopes whose product is 1. Line e has a slope of –2.