Write an equation given the slope and a point

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Presentation transcript:

Write an equation given the slope and a point EXAMPLE 2 Write an equation given the slope and a point Write an equation of the line that passes through (5, 4) and has a slope of – 3. SOLUTION Because you know the slope and a point on the line, use point-slope form to write an equation of the line. Let (x1, y1) = (5, 4) and m = – 3. y – y1 = m(x – x1) Use point-slope form. y – 4 = – 3(x – 5) Substitute for m, x1, and y1. y – 4 = – 3x + 15 Distributive property y = – 3x + 19 Write in slope-intercept form.

EXAMPLE 3 Write equations of parallel or perpendicular lines Write an equation of the line that passes through (–2,3) and is (a) parallel to, and (b) perpendicular to, the line y = –4x + 1. SOLUTION a. The given line has a slope of m1 = –4. So, a line parallel to it has a slope of m2 = m1 = –4. You know the slope and a point on the line, so use the point-slope form with (x1, y1) = (– 2, 3) to write an equation of the line.

Write equations of parallel or perpendicular lines EXAMPLE 3 Write equations of parallel or perpendicular lines y – y1 = m2(x – x1) Use point-slope form. y – 3 = – 4(x – (– 2)) Substitute for m2, x1, and y1. y – 3 = – 4(x + 2) Simplify. y – 3 = – 4x – 8 Distributive property y = – 4x – 5 Write in slope-intercept form.

Write equations of parallel or perpendicular lines EXAMPLE 3 Write equations of parallel or perpendicular lines b. A line perpendicular to a line with slope m1 = – 4 has a slope of m2 = – = . Use point-slope form with (x1, y1) = (– 2, 3) 1 4 m1 y – y1 = m2(x – x1) Use point-slope form. y – 3 = (x – (– 2)) 1 4 Substitute for m2, x1, and y1. y – 3 = (x +2) 1 4 Simplify. y – 3 = x + 1 4 2 Distributive property y = x + 1 4 2 Write in slope-intercept form.

GUIDED PRACTICE GUIDED PRACTICE for Examples 2 and 3 4. Write an equation of the line that passes through (– 1, 6) and has a slope of 4. SOLUTION Because you know the slope and a point on the line, use the point-slope form to write an equation of the line. Let (x1, y1) = (–1, 6) and m = 4 y – y1 = m(x – x1) Use point-slope form. y – 6 = 4(x – (– 1)) Substitute for m, x1, and y1. y – 6 = 4x + 4 Distributive property y = 4x + 10 Write in slope-intercept form.

GUIDED PRACTICE GUIDED PRACTICE for Examples 2 and 3 5. Write an equation of the line that passes through (4, –2) and is (a) parallel to, and (b) perpendicular to, the line y = 3x – 1. SOLUTION The given line has a slope of m1 = 3. So, a line parallel to it has a slope of m2 = m1 = 3. You know the slope and a point on the line, so use the point - slope form with (x1, y1) = (4, – 2) to write an equation of the line. y – y1 = m2(x – x1) Use point-slope form. y – (– 2) = 3(x – 4) Substitute for m2, x1, and y1. y + 2 = (x – 4) Simplify. y + 2 = 3x – 12 Distributive property y = 3x – 14 Write in slope-intercept form.

Use point - slope form with (x1, y1) = (4, – 2) GUIDED PRACTICE GUIDED PRACTICE for Examples 2 and 3 b. A line perpendicular to a line with slope m1 = 3 has a slope of m2 = – = – 1 1 3 m1 Use point - slope form with (x1, y1) = (4, – 2) y – y1 = m2(x – x1) Use point-slope form. y – (– 2) = – (x – 4) 1 3 Substitute for m2, x1, and y1. y + 2 = – (x – 4) 1 3 Simplify. 4 3 y + 2 = – x – 1 Distributive property y = – x – 1 3 2 Write in slope-intercept form.