Linear Equations in Slope Intercept Form Worksheet

Linear Equations in Slope Intercept Form Worksheet
  • Page 1
 1.  
What are the x and y intercepts of the line in the graph?


a.
x-intercept is - 2 and y-intercept is 2
b.
x-intercept is - 2 and y-intercept is - 2
c.
x-intercept is 2 and y-intercept is - 2
d.
x-intercept is 2 and y-intercept is 2


Solution:

The x-intercept is the x-coordinate of the point where a line crosses the x-axis.

In the figure, the line crosses the x-axis at x = 2.

So, the x-intercept of the line is 2.

The y-intercept is the y-coordinate of the point where a line crosses the y-axis.

In the figure, the line crosses the y-axis at y = 2.

So, the y-intercept of the line is 2.

The x and y intercepts of the line are 2 and 2 respectively.


Correct answer : (4)
 2.  
Find the equation of a line whose slope is 4 and y-intercept is 5.
a.
x = 5y - 4
b.
y = 4x + 5
c.
x = 4y + 5
d.
y = 5x - 4


Solution:

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

y = (4)x + (5)
[Substitute m = 4 and b = 5.]

y = 4x + 5
[Simplify the equation.]

The equation of the line in slope-intercept form is y = 4x + 5.


Correct answer : (2)
 3.  
Write the equation of the line whose slope is -4 and y-intercept is - 2 3.
a.
y = 4x - 2 3
b.
y = 4x + 2 3
c.
y = -4x - 2 3
d.
None of the above


Solution:

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

y = (-4)x + (- 23)
[Substitute m = - 4 and b = - 2 / 3.]

y = -4x - 23
[Simplify the equation.]

The equation of the line in slope-intercept form is y = -4x - 2 / 3.


Correct answer : (3)
 4.  
Is the equation (x-1) 1+ (y-3) 3= 24 + 42 in slope-intercept form?
a.
No
b.
Yes


Solution:

Compare the equation (x-1) / 1+ (y-3) / 3= 24 + 42 with the slope-intercept equation y = mx + b.

It is clear that the equation is not in the slope-intercept form.


Correct answer : (1)
 5.  
Identify the equation of the line in slope-intercept form for the graph shown.


a.
y = x - 3
b.
y = - x - 3
c.
y = - x + 3
d.
y = x + 3


Solution:

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

From the graph, (x1, y1) = (3, 0) and (x2, y2) = (0, - 3).

Slope m = y2 -y1x2 -x1

m = - 3 - 00 - 3
[Substitute the values of x1, y1, x2 and y2.]

m = - 3- 3 = 1
[Simplify the fraction.]

The graph of the line crosses the y-axis at (0, - 3).

The y-intercept is the y-coordinate of the point where a line crosses the y-axis.

y-intercept, b = - 3

y = (1)x + (- 3)
[Substitute the values of m and b in step 1.]

y = x - 3
[Simplify the equation.]

The equation of the line in slope-intercept form is y = x - 3.


Correct answer : (1)
 6.  
Is the equation y = 4x + 3 in slope-intercept form?
a.
No
b.
Yes


Solution:

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

The equation y = 4x + 3 is also in the same form as the equation in step 1, with slope 4 and y-intercept 3.

So, the equation y = 4x + 3 is in slope-intercept form.


Correct answer : (2)
 7.  
Find the slope of the line y = 2 3x + 1 3.
a.
2 3
b.
1 3
c.
3 4
d.
None of the above


Solution:

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

y = 23x + 13
[Given Equation.]

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

The slope of the line is 2 / 3.


Correct answer : (1)
 8.  
What is the y-intercept of the line y = -(4x) 5+ 5 6?
a.
4 6
b.
5 6
c.
4 5
d.
None of the above


Solution:

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

y = -(4x) / 5+ 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 : (2)
 9.  
What is the slope of the line in the graph?


a.
2
b.
-2
c.
3
d.
-3


Solution:

From the graph, (x1, y1) = (-1,0) and (x2, y2) = (0,-2).

Slope m = (y2 - y1) / (x2 - x1)

m = (-2-0)[0-(-1)]
[Substitute the values of x1, y1, x2 and y2.]

m = -2
[Simplify the fraction.]

The slope of the line shown in the graph is -2.


Correct answer : (2)
 10.  
Write the x and y intercepts of the line AB.

a.
x-intercept is -3 and y-intercept is -3
b.
x-intercept is -3 and y-intercept is 3
c.
x-intercept is 3 and y-intercept is -3
d.
None of the above


Solution:

The x-intercept is the x-coordinate of the point where a line crosses the x-axis.

In the figure, the line crosses the x-axis at x = -3.

So, the x-intercept of the line is -3.

The y-intercept is the y-coordinate of the point where a line crosses the y-axis.

In the figure, the line crosses the y-axis at y = 3.

So, the y-intercept of the line is 3.

The x and y intercepts of the line are -3 and 3.


Correct answer : (2)

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