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Graph Using Slope Intercept Form Worksheet

Graph Using Slope Intercept Form Worksheet
  • Page 1
 1.  
Find the slope of the line parallel to - 5x + 20y = 25.
a.
20
b.
1 5
c.
2
d.
1 4


Solution:

Two lines are said to be parallel if they have same slope and different y-intercepts.

The slope intercept form of the equation - 5x + 20y = 25 is y = 1 / 4x + 5 / 4.

The slope of the line - 5x + 20y = 25 is 1 / 4.

So, the slope of the line parallel to - 5x + 20y = 25 is 1 / 4.


Correct answer : (4)
 2.  
Write an equation for the line parallel to y + 3x = 6 and having y-intercept 10.
a.
x = - 3y + 10
b.
y = - 3x + 10
c.
- 6x + 3y = 10
d.
y = 6x + 10


Solution:

Two non-vertical lines are said to be parallel if they have same slope and different y-intercepts.

The slope intercept form of the equation is y = - 3x + 6.

The slope for the line y + 3x = 6 is, m = - 3.
[Compare with y = mx + c.]

The slope of the required line is - 3 and the y-intercept is 10.

So, the equation for the line parallel to y + 3x = 6 and having y-intercept 10 is y = - 3x + 10.


Correct answer : (2)
 3.  
What is the y-intercept of the line y = - 4x5 + 5 6?
a.
25
b.
- 4 5
c.
25 24
d.
5 6


Solution:

The slope-intercept form of the equation of a line with slope m and y-intercept b is y = mx + b.

y = - 4x5 + 5 / 6
[Given Equation.]

b = 56
[Compare the equation with slope-intercept form equation.]

The y-intercept of the line is 5 / 6.


Correct answer : (4)
 4.  
Which of the following lines are parallel?
a.
x - 5y - 19 = 0, - x - 5y + 9 = 0
b.
x + 5y - 19 = 0, x - 5y + 9 = 0
c.
x + 5y - 19 = 0, - x - 5y + 9 = 0
d.
x + 5y - 19 = 0, - x + 5y - 9 = 0


Solution:

Two lines which have the same slope and different y-intercepts are called parallel lines.

Write all the sets of equations in the standard slope-intercept form, y = mx + b and verify.

For the lines x + 5y - 19 = 0, - x - 5y + 9 = 0:

x + 5y - 19 = 0

y = - x5 + 195

Slope = - 1 / 5 and y-intercept = 19 / 5
[Compare with y = mx + b.]

- x - 5y + 9 = 0

y = - x5 + 95

Slope = - 1 / 5 and y-intercept = 9 / 5
[Compare with y = mx + b.]

Slopes are same and y-intercepts are different.

So, x + 5y - 19 = 0 and - x - 5y + 9 = 0 are parallel.


Correct answer : (3)
 5.  
Which of the following pairs of lines are parallel?
a.
- x + 74 y + 4 = 0, x - 74 y + 5 = 0
b.
- x - 74 y + 4 = 0, - x + 74 y - 5 = 0
c.
- x + 74 y + 4 = 0, - x - 74 y + 5 = 0
d.
x + 74 y + 4 = 0, x - 74 y + 5 = 0


Solution:

Two lines which have same slope and different y-intercepts, are said to be parallel.

Write all the sets of equations in the standard slope-intercept form, y = mx + b and verify.

For the lines - x + 7 / 4 y + 4 = 0, x - 7 / 4 y + 5 = 0:

- x + 74 y + 4 = 0

y = 47 x - 167

Slope = 4 / 7 and y-intercept = - 16 / 7
[Compare with y = mx + b.]

x - 74 y + 5 = 0

y = 47 x + 207

Slope = 4 / 7 and y-intercept = 20 / 7
[Compare with y = mx + b.]

Slopes are same and y-intercepts are different.

So, - x + 7 / 4 y + 4 = 0 and x - 7 / 4 y + 5 = 0 are parallel.


Correct answer : (1)
 6.  
In the slope-intercept form y = mx + b, m is ______ and b is ______.
a.
y-intercept, slope
b.
x-intercept, slope
c.
slope, x-intercept
d.
slope, y-intercept


Solution:

The equation of the line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.


Correct answer : (4)
 7.  
Find the slope of the graph of the equation y = 2 3x + 2 5.
a.
2 5
b.
- 2 3
c.
4 5
d.
2 3


Solution:

The slope-intercept form of the equation of a line with slope m and y-intercept b is y = mx + b.

y = 23x + 25
[Given Equation.]

m = 23
[Compare the equation with slope-intercept form equation.]

The slope of the line is 2 / 3.


Correct answer : (4)
 8.  
Find the slope (m) and y-intercept (b) of the graph of the equation 7x + 3y = 14.
a.
m = 73, b = - 143
b.
m = - 73, b = 143
c.
m = 73, b = 143
d.
m = 7, b = 14


Solution:

7x + 3y = 14
[Write original equation.]

3y = - 7x + 14
[Subtract 7x from each side.]

y = - 73 x + 143
[Divide each side by 3.]

The equation is in slope-intercept form y = mx + b

The slope is - 73 and y-intercept is 143.
[ m = - 73, b = 143.]


Correct answer : (2)
 9.  
A Painting exhibition is being organized in Redfield. The painters who wish to exhibit and sell their paintings need to pay $100 for the space and $20 for each painting they sell. The equation 20x - y + 100 = 0 models the above situation, where y is the total amount paid to the organizers and x is the number of paintings each painter sells. What is the y-intercept of this model? Interprete the meaning of y-intercept.
a.
20; charge for each paint sold
b.
- 100; space charge for exhibiting the paints
c.
20x + 100; charge for each paint sold
d.
100; space charge for exhibiting the paints


Solution:

20x - y + 100 = 0

20x + 100 = y
[Rearrange the terms.]

The equation is in slope-intercept form y = mx + b, where y - intercept is b.

y-intercept is 100, which is the space charge for exhibiting the paints.
[b = 100.]


Correct answer : (4)
 10.  
Which graph represents the equation 3x + 5y + 6 = 1 + x?

a.
Graph 3
b.
Graph 4
c.
Graph 2
d.
Graph 1


Solution:

3x + 5y + 6 = 1 + x
[Write original equation.]

5y = - 2x - 5
[Subtract 3x + 6 from each side.]

y = - 25 x - 1
[Divide each side by 5.]

The equation is in slope-intercept form y = mx + b.

The slope is - 25 and y-intercept is - 1.
[m = - 25, b = - 1.]

Plot the point (0, b) when b is - 1.

Use the slope to locate a second point on line.

m = - 25 = riserun move 2 units downmove 5 unit right


Draw a line through the two points.

Graph of the equation 3x + 5y + 6 = 1 + x matches with Graph 1.


Correct answer : (4)

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