Quick Graphing Using Slope-Intercept Form

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In addition to level 3.0 and above and beyond what was taught in class,  the student may:· Make connection with other concepts in math· Make connection with other content areas.

The student will understand that linear relationships can be described using multiple representations. - Represent and solve equations and inequalities graphically. - Write equations in slope-intercept form, point-slope form, and standard form. - Graph linear equations and inequalities in two variables. - Find x- and y-intercepts.

The student will be able to: - Calculate slope. - Determine if a point is a solution to an equation. - Graph an equation using a table and slope-intercept form. 

With help from theteacher, the student haspartial success with calculating slope, writing an equation in slope-intercept form, and graphing an equation.

Even with help, the student has no success understanding the concept of a linear relationships.

Learning Goal #1 for Focus 4 (HS.A-CED.A.2, HS.REI.ID.10 & 12, HS.F-IF.B.6,

HS.F-IF.C.7, HS.F-LE.A.2): The student will understand that linear relationships can be described using multiple representations.

What are the different methods we have used to graph a line?

• Plot points

• Make a table• Find the x and y- intercepts

• Plot a point then graph the slope.

Slope-intercept form: linear equation

y = mx+b

m represents the slope of the line

b represents the y-intercept *where the line crosses the y-axis

You can tell by looking at the equation not only where the line crosses y, but whether it

has a positive or negative slope.

If m is positive the slope is positive, and your line will go up from left to right.

If m is negative, the slope is negative and your line will go down from left to right.

y = mx + b

Determine what is the slope, y-intercept,

and direction of each equation.

1. y = 3x + 4

2. y = ½ x – 9

3. y = -4/5 x + 7

4. y = -2x - 4

1. Slope = 3 y-intercept = (0, 4)goes up left to right

2. Slope = ½ y-intercept = (0, -9) goes up left to right

3. Slope = -4/5 y-intercept = (0, 7) goes down left to right

4. Slope = -2 y-intercept = (0, -4) goes down left to right

When your equation is not in slope intercept form, rewrite it into slope-intercept form

(y=mx+b). 2x = 5y - 10

• 2x = 5y-10-5y -5y

• 2x – 5y = -10-2x -2x

• -5y = -2x – 10-5 -5 -5

• y = 2/5x + 2

What is the y- intercept?

(0,2)

What is the slope? 2/5

What direction will the line go?

Up, from

left to right.

Graph the line y = 2/5x + 2The slope is 2/5 & the y-intercept is 2.

1234

-4-3

-2

-1-4 -3 -2-1 1 2 3 4 5 6

Steps to graphing a line in slope intercept form:

1. Plot the y-intercept. (0,2)

2. Count up 2 right 5 and plot next point.

3. Connect the dots.

Graph the line 2y = -2x + 6

1. Change to slope intercept form.

2. y = -x + 33. y-intercept (0,3)4. Slope -15. Line will go down

from left to right.

1234

-4-3

-2

-1-4 -3 -2-1 1 2 3 4 5 6

Special line:

• Parallel Lines: lines have the same slope, but different y-intercept (b value)

• y = 2x + 4 and y = 2x – 3 are parallel lines.

Graph y = -x+6 and y = -x+2 on the same graph.

Notice that they each have the same slope of -1, but they cross y at different

spots.

y = -x + 6

y = -x + 2