Bell Work

Solve for “y”

1.) 3x – 2y = -8

2.) 5x – y + 12 = 3x + 10

3.) 3x – 4y = -7y – 12

Slope of a Line

Slope – The ratio of the change in value of the y-coordinates over the change in value of the x-coordinates for any two points on a line.

Slope is represented by the letter “m”.

Slope Formulas:

rise

run

y1 y 2

x1 x 2

Bell Work

1. -5x + 4y = -16

2. 3x – 6y = 12 + 2x

3. 2(-2x – y) = 3x + 4

Special Slopes

Horizontal lines have a slope of zero. (Zero is in the top of the fraction.)

Vertical lines have a slope that is undefined. (Zero is in the bottom of the fraction.)

Bell WorkBell Work

Determine the slope using the two Determine the slope using the two points given.points given.

1.) (3, 6), (1, 3)1.) (3, 6), (1, 3) 2.) (-2, 4), (3, 2)2.) (-2, 4), (3, 2)

3.) (-1, 3), (-1, 5)3.) (-1, 3), (-1, 5) 4.) (-2, 4), (-3, 4)4.) (-2, 4), (-3, 4)

Rise over Run TriangleRise over Run Triangle

May determine the slope of a line May determine the slope of a line by determining the rise and run by determining the rise and run from two points on the line.from two points on the line.

A line has a positive slope if the A line has a positive slope if the line is rising from left to right.line is rising from left to right.

A line has a negative slope if the A line has a negative slope if the line is going down from left to line is going down from left to right.right.

Steps for doing Rise over Run Steps for doing Rise over Run TriangleTriangle

1.) Find two points on the line.1.) Find two points on the line.

2.) Create a right triangle using the two points.2.) Create a right triangle using the two points.

3.) Determine the rise and the run and put in 3.) Determine the rise and the run and put in fraction form (rise on top, run on bottom).fraction form (rise on top, run on bottom).

4.) Determine if the slope is positive or negative.4.) Determine if the slope is positive or negative.

5.) Reduce the fraction if possible.5.) Reduce the fraction if possible.

Slope-Intercept FormSlope-Intercept Form

y = mx + by = mx + b

m = slopem = slope

b = y-interceptb = y-intercept

Slope-Intercept FormSlope-Intercept Form

An equation is in slope-intercept An equation is in slope-intercept form if the equation is solved for “y”.form if the equation is solved for “y”.

The number in front of “x” is the The number in front of “x” is the slope.slope.

The number by itself is the “y-The number by itself is the “y-intercept.”intercept.”

““b” is used to represent y-intercept.b” is used to represent y-intercept.y = mx + by = mx + b

Graphing a Line using the Graphing a Line using the slope and a pointslope and a point

1.1. Get the equation in slope-int. & Get the equation in slope-int. & identify “m” & “b”.identify “m” & “b”.

2.2. Plot the y-intercept.Plot the y-intercept.3.3. Plot the second point using the slope Plot the second point using the slope

from the y-intercept.from the y-intercept.a)a) Top # determines how many you go Top # determines how many you go

up or down from the point. Positive up or down from the point. Positive goes up. Negative goes down.goes up. Negative goes down.

b)b) Bottom # determines how many you Bottom # determines how many you go to the right.go to the right.

4.4. Connect the points.Connect the points.

Bell WorkBell Work

Get “y” by itself.Get “y” by itself.

1. 3x – 2y = 61. 3x – 2y = 6

2. ½ y – 2x = -32. ½ y – 2x = -3

3. 3x + 4y – 5 = 5x + 4 3. 3x + 4y – 5 = 5x + 4

Graphing Using Intercepts

x-intercept – The point where a line crosses the x-axis. (x, 0) is the ordered pair.

y-intercept – The point where a line crosses the y-axis. (0, y) is the ordered pair.

2x + 3y = -6

Get the equation in standard form.

To find the x-intercept, substitute 0 for “y” in the equation given and find what “x” is equal to.

To find the y-intercept, substitute 0 for “x” in the equation given and find what “y” is equal to.

To graph the line, plot the x-intercept and the y-intercept and then connect the dots.