1. Writing Equations of a Line

2. Various Forms of an Equation of a Line.
Gradient-Intercept Form
Standard Form
Point-Gradient Form

3. EXAMPLE 1
Write an equation given the slope and y-intercept
Write an equation of the line shown.

4. Write an equation given the slope and y-intercept
EXAMPLE 1
Write an equation given the slope and y-intercept
SOLUTION
From the graph, you can see that the slope is m = and the y-intercept is c = –2. Use slope-intercept form to write an equation of the line. 3 4
y = mx + c
Use gradient-intercept form.
y = x + (–2) 3 4
Substitute for m and –2 for b. 3 4 3 4
y = x (–2)
Simplify.

5. GUIDED PRACTICE
for Example 1
Write an equation of the line that has the given slope and y-intercept.
1. m = 3, b = 1
3. m = – , b = 3 4 7 2
ANSWER
ANSWER
y = – x + 3 4 7 2
y = x + 1 3
2. m = –2 , b = –4
ANSWER
y = –2x – 4

6. 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 gradient 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.

7. 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.

8. 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.

9. 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
Write in slope-intercept form.

10. 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.
ANSWER
y = 4x + 10
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.
ANSWER
y = 3x – 14

11. EXAMPLE 4
Write an equation given two points
Write an equation of the line that passes through (5, –2) and (2, 10).
SOLUTION
The line passes through (x1, y1) = (5,–2) and
(x2, y2) = (2, 10). Find its slope.
y2 – y1
m =
x2 – x1
10 – (–2) =
2 – 5 12 –3
= –4

12. Write an equation given two points
EXAMPLE 4
Write an equation given two points
You know the slope and a point on the line, so use point-slope form with either given point to write an equation of the line. Choose (x1, y1) = (4, – 7).
y2 – y1 = m(x – x1)
Use point-slope form.
y – 10 = – 4(x – 2)
Substitute for m, x1, and y1.
y – 10 = – 4x + 8
Distributive property
y = – 4x + 8
Write in slope-intercept form.