GRAPHING LINEAR EQUATIONS IN SLOPE INTERCEPT FORM WORKSHEET

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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