Graphing Linear Equations Unit Review

Unit Review - Graphing Linear Equations

Before we graph two lines, lets make sure you can graph one line properly!​

I should be able to

Graphing a Point

Always written in the form (x,y)

​

The x-value tells us to

move left or right

​

The y-value tells us to

move up or down

​

Graph (4,6)​

​

Graphing

Graph the following points:

(7, -3)

(-4, 5)

(8, 6)

(-3, -9)

Drag and Drop

The coordinates of point P are ​

Placeholder

, point N are ​

Placeholder

, S are ​

Placeholder

and M are ​

Placeholder

Drag these tiles and drop them in the correct blank above

(2,-3)

(6,0)

(-9,0)

(7,-9)

(-3,2)

(0,6)

(-9,7)

(0,-9)

Identifying Basic Slopes

Slope: the 'steepness' of a line.

​

There are FOUR basic categories for SLOPES

POSITIVE SLOPE

NEGATIVE SLOPE

SLOPE OF ZERO

UNDEFINED SLOPE

Match

Match the Graph with its slope.

Negative

Positive

Zero

Undefined

• Negative

• Positive

• Zero

• Undefined

Remember, you can use rise/run to find the slope of any graph.

​

​Some text here about the topic of discussion.

slope of a graph

Multiple Choice

Find the slope. Determine if the line is negative or positive. Then, count rise over run.

• 3/4

• 4/3

• -3/4

• -4/3

Multiple Choice

What is the slope of this line?

$$slope=\frac{\text{rise}}{\text{run}}$$  

• $$\frac{1}{4}$$  

• $$-\frac{1}{4}$$  

• $$\frac{4}{1}$$  

• $$-\frac{4}{1}$$  

We talked about how to use this formula to find the slope between any 2 points.

​

You should be able to memorize this for the test! ​

​

​Some text here about the topic of discussion.

Slope formula

Multiple Choice

Find the slope of the line that goes through the points

(−1,−2) and (−3,−4).

• 1

• 2

• 3

• 4

Multiple Choice

Find the slope of the line that passes through the points 

(2, 4) and (6, 12).

• $$\frac{1}{2}$$

• 2

• $$-\frac{1}{2}$$

• -2

Remember, "m" is the same as the constant or the unit rate. In this equation, it is the "slope".

The y-intercept determines where the line starts on ​coordinate plane and if it is a proportional relationship or not.

Slope-intercept form

Multiple Choice

What does the "m" variable represent in the linear equation y=mx+b

• y-intercept

• slope

• the initial value

• x

Multiple Choice

What is the correct equation for the given information?

Slope = 3

Y-Intercept = 2

• y = 2x + 3

• y = 1/2x + 3

• y = 3x - 2

• y = 3x + 2

Graphing

Graph:

$$y=\frac{2}{3}x-4$$

Hint: Drag one point to the y-intercept first. Then drag the other point after counting the slope.

Find the Equation of the Line.

• Things to look for:

• Is the line positive or negative? (is it going up or down?)

• Look at the y-intercept, where does it cross the y-axis?

Multiple Choice

Write the equation of the line.

• $$y=-\frac{2}{3}x+4$$

• $$y\ =\ \frac{2}{3}x+4$$

• $$y=-\frac{3}{2}x+4$$

• $$y=\frac{3}{2}x+4$$

Drag and Drop

Given:  $$y=\frac{3}{5}x$$ , the slope is ​

Placeholder

and the y-intercept is ​

Placeholder

Drag these tiles and drop them in the correct blank above

0

1

Math Response

Write the equation of the line in Slope-Intercept Form. ( $$y=mx+b$$ )

Type answer here

Correct Answer: y=-\frac{3}{4}x-3

Deg^°

Rad

X and Y Intercepts

Linear equations have x and y-intercepts. The x-intercept is the x-coordinate of the point at which the graph crosses the x-axis. The y-intercept is the y-coordinate of the point at which the graph crosses the y-axis. 

X and Y intercepts

• x-intercept: What x is when y is 0? Where does the line cross the x-axis?

• y-intercept: What y is when x is 0? Where does the line cross the y-axis?

Multiple Choice

What is the x-intercept of the graph?

• (5,0)

• (0,5)

• (0,4)

• (4,0)

Multiple Choice

What is the y-intercept?

• (0,15)

• (3,0)

• (15,0)

• (0,3)

Drag and Drop

The line graphed has an x-intercept of ​

Placeholder

and a y-intercept of ​

Placeholder

.

Drag these tiles and drop them in the correct blank above

(1,0)

(0,-4)

(-4,0)

(0,1)

(1,-4)

(-4,1)

​Standard Form

Multiple Choice

Which of these represents standard form?

• y - y₁ = m(x-x₁)

• Ax + By = C

• y = mx + b

Multiple Choice

What is the x-intercept? (set y=0)

$$4x-2y=-8$$  

• -2

• 2

• 4

• -8

Multiple Choice

What is the y-intercept? (set x=0)

$$4x-2y=-8$$  

• -2

• 2

• 4

• -8

Solving equations for y

• Get y by itself (shown in the next slide)

• Solving for y will give you an equation in the form y = mx + b

• Slope of the line is m (the coefficient on x)

• The y-intercept is b (the constant term)

In this equation, what is the slope? What is the y-intercept?

Multiple Choice

what is the first step to solve for slope intercept form on

-x + 4y = 11

• subtract 11 from both sides

• add x to both sides

• subtract x from both sides

• put in th y=

Multiple Choice

Convert the standard form equation into slope-intercept form.
x + 5y = -25

• y = -⅕x - 5

• y = -x - 5

• x = 20

• y = 27, 239, 430

Math Response

Convert to slope intercept form:

$$10x-6y=30$$

Type answer here

Correct Answer: y=\frac{5}{3}x-5

Deg^°

Rad

Match

Match the following

• The coordinate where the function crosses the x-axis. At this point, y=0.

• The coordinate where the function crosses the y-axis. At this point, x=0.

• Measure of how STEEP a line is, can be found using rise/run

• Slope-intercept form

• Standard Form

x-intercept

y-intercept

SLOPE

y=mx+b

Ax+By=C

• x-intercept

• y-intercept

• SLOPE

• y=mx+b

• Ax+By=C

Poll

From 1-4, how comfortable are you with graphing a linear equation?

• 1- I have no idea whats going on

• 2-I have an idea but still need alot of practice

• 3-I feel comfortable with it

• 4-Im ready to teach this to someone else.