1. 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.

2. 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.

3. 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.

4. 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.

5. 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.

6. 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.

7. 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.