Warm-up

You are driving on a road trip and you want to find out how many hours total it will take you to get to California. After driving for 4 hours, you were 280 miles from home. You are now 520 miles from home and have driven for 8 hours. How long will it take you to drive 3000 miles?

Writing Equations of

Lines

3 Forms

Slope-InterceptPoint-SlopeStandard

**Always have the variables x & y**

Break into groups of 4.

Slope Intercept

y mx b m is the slope of the line

b is the y-intercept of the line

Example

1) Write the equation of the line that has a slope of 4, and a y-intercept of -2.

2) Write the equation of the line between the points (2, 4) and (4, 12).

Example

3) Write the equation of the line pictured.

Point-Slope

1 1( )y y m x x

(x1, y1) is a point on the line

m is the slope of the line

Examples

4) Write the equation of the line that passes through the point (4, -2) and has a slope of 6.

5) Write the equation of the line that passes through the points (1, 8) and (-2, 6).

Standard Form

Ax By C Where A, B & C are integers

A is NOT negative

Putting Equations into Standard Form

1) Put the equation into slope-intercept form.

2) Subtract mx from both sides (EX: y = 3x + 7 becomes –3x + y = 7)

3) If the number in front of x is negative, multiply everything by -1.

4) If the number in front of x is a fraction, multiply everything by the denominator.

Examples6) Write the equation of the line that

passes through the points (2, 6) and (3, -3) in standard form.

7) Write the equation of the line that has slope -5 and passes through the point (1, -4) in standard form.

8) Write the equation of the line through the points (3, -5) and (7, 1) in standard form.

Pop Quiz• You are given the slope of a line and a

point on the line. How can you find an equation of the line?

• You are given the slope of a line and the y-intercept of the line, how can you find an equation of the line?

• You are given the x-intercept and the y-intercept of a line, how can you find an equation of the line?

WRITE THIS

1) Given slope (m) and y int (b): plug into y = mx + b

2) Given slope (m) and a point (x, y): plug into y = mx + b to find b. Then go to step 1.

3) Given two points (x1,y1) and (x2, y2): First find slope, then go to step 2.

Exit Ticket

9) Write the equation of the line perpendicular to the line y = ½ x + 8 through the point (1, -7) in all 3 forms.

Flipped

Slope Intercept

y mx b m is the slope of the line

b is the y-intercept of the line

Example

1) Write the equation of the line that has a slope of 4, and a y-intercept of -2.

2) Write the equation of the line between the points (2, 4) and (4, 12).

Example

3) Write the equation of the line pictured.

Point-Slope

1 1( )y y m x x

(x1, y1) is a point on the line

m is the slope of the line

Examples

4) Write the equation of the line that passes through the point (4, -2) and has a slope of 6.

5) Write the equation of the line that passes through the points (1, 8) and (-2, 6).

Standard Form

Ax By C Where A, B & C are integers

A is NOT negative

Putting Equations into Standard Form

1) Put the equation into slope-intercept form.

2) Subtract mx from both sides (EX: y = 3x + 7 becomes –3x + y = 7)

3) If the number in front of x is negative, multiply everything by -1.

4) If the number in front of x is a fraction, multiply everything by the denominator.

Examples6) Write the equation of the line that

passes through the points (2, 6) and (3, -3) in standard form.

7) Write the equation of the line that has slope -5 and passes through the point (1, -4) in standard form.

8) Write the equation of the line through the points (3, -5) and (7, 1) in standard form.

Pop Quiz• You are given the slope of a line and a

point on the line. How can you find an equation of the line?

• You are given the slope of a line and the y-intercept of the line, how can you find an equation of the line?

• You are given the x-intercept and the y-intercept of a line, how can you find an equation of the line?