lines

Lines y

xO 2 4 6

2

4

6

–6

–4

–2–6 –4 –2

How do you graph the line and find its equation when

1. You are given the y-intercept and the slope.

Example: y-intercept is 1 and slope is 2/3. Equation:

2. You are given a point and the slope.

Example: point is (–2, 3) and slope is –3. Equation:

3. You are given two points.

Example: 1st point is (3, –4) and 2nd point is (2, 1). Equation:

Slope-Intercept Form:

where m is the slope and b is the y-intercept

Example:

y = x – 3

Point-Slope Form:

where (x1, y1) is the point and m is the slope

Example:

y – 1 = 2(x – 2)

General Form:

Example:

4x – 3y = 12

Two-Intercepts Form:

where a is the x-intercept and b is the y-intercept

Example:

y

xO 2 4 6

2

4

6

–6

–4

–2–6 –4 –2

y

xO 2 4 6

2

4

6

–6

–4

–2–6 –4 –2

y

xO 2 4 6

2

4

6

–6

–4

–2–6 –4 –2

y

xO 2 4 6

2

4

6

–6

–4

–2–6 –4 –2

3

21

23

yx

// Lines and Lines:

1st: Sketch y = ¾x + 1

2nd: Sketch the line parallel to it, and have y-intercept = –2.Q: What is the slope?

Q: What is the equation?

3rd: Sketch the line perpendicularto it and have y-intercept = 4.Q: What is the slope?

Q: What is the equation?

y

xO 2 4 6

2

4

6

–6

–4

–2–6 –4 –2