Graphing linear equations by slope intercept worksheet answers

Video transcript

We are asked to graph y is equal to 1/3x minus 2. Now, whenever you see an equation in this form, this is called slope-intercept form. And the general way of writing it is y is equal to mx plus b, where m is the slope. And here in this case, m is equal to 1/3-- so let me write that down-- m is equal to 1/3, and b is the y-intercept. So in this case, b is equal to negative 2. And you know that b is the y-intercept, because we know that the y-intercept occurs when x is equal to 0. So if x is equal to 0 in either of these situations, this term just becomes 0 and y will be equal to b. So that's what we mean by b is the y-intercept. So whenever you look at an equation in this form, it's actually fairly straightforward to graph this line. b is the y-intercept. In this case it is negative 2, so that means that this line must intersect the y-axis at y is equal to negative 2, so it's this point right here. Negative 1, negative 2, this is the point 0, negative 2. If you don't believe me, there's nothing magical about this, try evaluating or try solving for y when x is equal to 0. When x is equal to 0, this term cancels out and you're just left with y is equal to negative 2. So that's the y-intercept right there. Now, this 1/3 tells us the slope of the line. How much do we change in y for any change in x? So this tells us that 1/3, so that right there, is the slope. So it tells us that 1/3 is equal to the change in y over the change in x. Or another way to think about it, if x changes by 3, then y would change by 1. So let me graph that. So we know that this point is on the graph, that's the y-intercept. The slope tells us that if x changes by 3-- so let me go 3 three to the right, 1, 2, 3-- that y will change by 1. So this must also be a point on the graph. And we could keep doing that. If x changes by 3, y changes by 1. If x goes down by 3, y will go down by 1. If x goes down by 6, y will go down by 2. It's that same ratio, so 1, 2, 3, 4, 5, 6, 1, 2. And you can see all of these points are on the line, and the line is the graph of this equation up here. So let me graph it. So it'll look something like that. And you're done.

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Put your utmost energy into our free worksheets on graphing lines in slope-intercept form! Each pdf consists of nine problems that allow students to observe equations given in the slope-intercept form and graph them to their heart's content. Each equation is in the form y = mx + b, where m is the slope of the line and b is the y-intercept. First, pin the point b. Next, substitute x with an integer to find the value of y. Pin the obtained value and use both the points to graph a line. The two (x,y) points make graphing equations in slope-intercept form an easy affair.

These printable resources are useful for grade 8 and high school students.

CCSS: HSA-CED

Graph the following linear equations.

Problem 1 :

y  =  2x + 1

Problem 2 :

y  =  -1.5x + 2

Problem 3 :

x - y - 2  =  0

Problem 4 :

5x + y  =  3

Answers

1. Answer :

y  =  2x + 1

The equation 'y  =  2x + 1' is in the form of 

y  =  mx + b

Then, 

m  =  2

b  =  1

Because slope '2' is a positive value, the line will be a rising line.

And also,

rise / run  =  2

rise / run  =  2 / 1

Then,

rise  =  2

run  =  1

Because the y-intercept is 1, the line will intersect y-axis at 1. 

Graphing : 

Step 1 :

Plot the y-intercept at (0, 1). 

Step 2 :

Because the run is 1, move 1 unit to the right from (0, 1).

Step 3 :

Because the rise is 2 and the line is rising line, move 2 units up from the position reached in step 2.   

Now, you are at (1, 3). 

Connect the points (0, 1) and (1, 3) to get the line.  

2. Answer :

y  =  -1.5x + 2

The equation 'y  =  -1.5x + 2' is in the form of 

y  =  mx + b

Then, 

m  =  -1.5

b  =  2

Because slope '-1.5' is a negative value, the line will be a falling line.

And also,

rise / run  =  1.5

rise / run  =  3 / 2 

Then,

rise  =  3

run  =  2

Because the y-intercept is 2, the line will intersect y-axis at 2. 

Graphing : 

Step 1 :

Plot the y-intercept at (0, 2). 

Step 2 :

Because the run is 2, move 2 units to the right from (0, 2).

Step 3 :

Because the rise is 3 and the line is falling line, move 3 units down from the position reached in step 2.   

Now, you are at (2, -1). 

Connect the points (0, 2) and (2, -1) to get the line.  

3. Answer :

x - y - 2  =  0

The equation 'x - y - 2  =  0' is not slope -intercept form. 

Write the given equation in slope-intercept form. 

x - y - 2  =  0

Add y to each side. 

x - 2  =  y

or 

y  =  x - 2

The equation 'y  =  x - 2' is in the form of 

y  =  mx + b

Then, 

m  =  1

b  =  -2

Because slope '1' is a positive value, the line will be a rising line.

And also,

rise / run  =  1

rise / run  =  1 / 1 

Then,

rise  =  1

run  =  1

Because the y-intercept is -2, the line will intersect y-axis at -2. 

Graphing : 

Step 1 :

Plot the y-intercept at (0, -2). 

Step 2 :

Because the run is 1, move 1 unit to the right from (0, -2).

Step 3 :

Because the rise is 1 and the line is rising line, move 1 unit up from the position reached in step 2.   

Now, you are at (1, -1). 

Connect the points (0, -2) and (1, -1) to get the line.  

4. Answer :

5x + y  =  3

The equation '5x + y  =  3' is not slope -intercept form. 

Write the given equation in slope-intercept form. 

5x + y  =  3

Subtract 5x from each side. 

y  =  3 - 5x

y  =  -5x + 3

The equation 'y  =  -5x + 3' is in the form of 

y  =  mx + b

Then, 

m  =  -5

b  =  3

Because slope '-5' is a negative value, the line will be a falling line.

And also,

rise / run  =  5

rise / run  =  5 / 1 

Then,

rise  =  5

run  =  1

Because the y-intercept is 3, the line will intersect y-axis at 3. 

Graphing : 

Step 1 :

Plot the y-intercept at (0, 3). 

Step 2 :

Because the run is 1, move 1 unit to the right from (0, 3).

Step 3 :

Because the rise is 5 and the line is falling line, move 5 units down from the position reached in step 2.   

Now, you are at (1, -2). 

Connect the points (0, 3) and (1, -2) to get the line.  

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