Linear Algebra - GED Math
Card 0 of 730
Find the slope and y-intercept of the line depicted by the equation:

Find the slope and y-intercept of the line depicted by the equation:
The equation is written in slope-intercept form, which is:

where
is equal to the slope and
is equal to the y-intercept. Therefore, a line depicted by the equation

has a slope that is equal to
and a y-intercept that is equal to
.
The equation is written in slope-intercept form, which is:
where is equal to the slope and
is equal to the y-intercept. Therefore, a line depicted by the equation
has a slope that is equal to and a y-intercept that is equal to
.
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Find the slope and y-intercept of the line that is represented by the equation 
Find the slope and y-intercept of the line that is represented by the equation
The slope-intercept form of a line is:
, where
is the slope and
is the y-intercept.
In this equation,
and 
The slope-intercept form of a line is: , where
is the slope and
is the y-intercept.
In this equation, and
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What is the slope and y-intercept of the following line?

What is the slope and y-intercept of the following line?
Convert the equation into slope-intercept form, which is
, where
is the slope and
is the y-intercept.







Convert the equation into slope-intercept form, which is , where
is the slope and
is the y-intercept.
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Refer to above red line. What is its slope?
Refer to above red line. What is its slope?
Given two points,
, the slope can be calculated using the following formula:

Set
:

Given two points, , the slope can be calculated using the following formula:
Set :
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The grade of a road is defined as the slope of the road expressed as a percent as opposed to a fraction or decimal.
A road is graded so that for every 40 feet of horizontal distance, the road rises 6 feet. What is the grade of the road?
The grade of a road is defined as the slope of the road expressed as a percent as opposed to a fraction or decimal.
A road is graded so that for every 40 feet of horizontal distance, the road rises 6 feet. What is the grade of the road?
The slope is the ratio of the vertical change (rise) to the horizontal change (run), so the slope of the road, as a fraction, is
. Multiply this by 100% to get its equivalent percent:

This is the correct choice.
The slope is the ratio of the vertical change (rise) to the horizontal change (run), so the slope of the road, as a fraction, is . Multiply this by 100% to get its equivalent percent:
This is the correct choice.
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What is the slope of the line perpendicular to
?
What is the slope of the line perpendicular to ?
In order to find the perpendicular of a given slope, you need that given slope! This is easy to compute, given your equation. Just get it into slope-intercept form. Recall that it is 
Simplifying your equation, you get:


This means that your perpendicular slope (which is opposite and reciprocal) will be
.
In order to find the perpendicular of a given slope, you need that given slope! This is easy to compute, given your equation. Just get it into slope-intercept form. Recall that it is
Simplifying your equation, you get:
This means that your perpendicular slope (which is opposite and reciprocal) will be .
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What is the equation of a line with a slope perpendicular to the line passing through the points
and
?
What is the equation of a line with a slope perpendicular to the line passing through the points and
?
First, you should solve for the slope of the line passing through your two points. Recall that the equation for finding the slope between two points is:

For your data, this is

Now, recall that perpendicular slopes are opposite and reciprocal. Therefore, the slope of your line will be
. Given that all of your options are in slope-intercept form, this is somewhat easy. Remember that slope-intercept form is:

is your slope. Therefore, you are looking for an equation with 
The only option that matches this is:

First, you should solve for the slope of the line passing through your two points. Recall that the equation for finding the slope between two points is:
For your data, this is
Now, recall that perpendicular slopes are opposite and reciprocal. Therefore, the slope of your line will be . Given that all of your options are in slope-intercept form, this is somewhat easy. Remember that slope-intercept form is:
is your slope. Therefore, you are looking for an equation with
The only option that matches this is:
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What is the x-intercept of
?
What is the x-intercept of ?
Remember, to find the x-intercept, you need to set
equal to zero. Therefore, you get:

Simply solving, this is 
Remember, to find the x-intercept, you need to set equal to zero. Therefore, you get:
Simply solving, this is
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Find the slope of the line that has the equation: 
Find the slope of the line that has the equation:
Step 1: Move x and y to opposite sides...
We will subtract 2x from both sides...
Result, 
Step 2: Recall the basic equation of a line...
, where the coefficient of y is
.
Step 3: Divide every term by
to change the coefficient of y to
:

Step 4: Reduce...

Step 5: The slope of a line is the coefficient in front of the x term...
So, the slope is 
Step 1: Move x and y to opposite sides...
We will subtract 2x from both sides...
Result,
Step 2: Recall the basic equation of a line...
, where the coefficient of y is
.
Step 3: Divide every term by to change the coefficient of y to
:
Step 4: Reduce...
Step 5: The slope of a line is the coefficient in front of the x term...
So, the slope is
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Find the slope of the following equation: 
Find the slope of the following equation:
In order to find the slope, we will need the equation in slope-intercept form.

Distribute the negative nine through the binomial.

The slope is: 
In order to find the slope, we will need the equation in slope-intercept form.
Distribute the negative nine through the binomial.
The slope is:
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What is the y-intercept of the following equation? 
What is the y-intercept of the following equation?
The y-intercept is the value of
when
.
Substitute the value of zero into
, and solve for
.


Subtract 7 from both sides.


The answer is: 
The y-intercept is the value of when
.
Substitute the value of zero into , and solve for
.
Subtract 7 from both sides.
The answer is:
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Find the slope and y-intercept, respectively, given the following equation:

Find the slope and y-intercept, respectively, given the following equation:
Rewrite the equation in slope-intercept format: 
Divide by negative two on both sides. This is also the same as multiplying both sides by negative half.


Rearrange the terms.

The slope is: 
The y-intercept is: 
The answer is: 
Rewrite the equation in slope-intercept format:
Divide by negative two on both sides. This is also the same as multiplying both sides by negative half.
Rearrange the terms.
The slope is:
The y-intercept is:
The answer is:
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Find the slope of the following function: 
Find the slope of the following function:
Simplify the terms of the equation by distribution.


Subtract the terms.

The equation is now in slope-intercept form, where
.
The slope is
.
The answer is
.
Simplify the terms of the equation by distribution.
Subtract the terms.
The equation is now in slope-intercept form, where .
The slope is .
The answer is .
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What is the slope of the following equation? 
What is the slope of the following equation?
To determine the slope, we will need the equation in slope-intercept form.

Subtract
on both sides.


Divide by 9 on both sides.

Split both terms on the right side.

The slope is: 
To determine the slope, we will need the equation in slope-intercept form.
Subtract on both sides.
Divide by 9 on both sides.
Split both terms on the right side.
The slope is:
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Identify the y-intercept: 
Identify the y-intercept:
In order to find the y-intercept, we will need to let
and solve for
.


Subtract
from both sides. Do NOT divide by
on both sides.


The answer is: 
In order to find the y-intercept, we will need to let and solve for
.
Subtract from both sides. Do NOT divide by
on both sides.
The answer is:
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What is the x-intercept of the following equation? 
What is the x-intercept of the following equation?
In order to find the x-intercept, we will need to let
, and solve for
.

Add
on both sides.


Divide by five on both sides.

The answer is: 
In order to find the x-intercept, we will need to let , and solve for
.
Add on both sides.
Divide by five on both sides.
The answer is:
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A line on the coordinate plane has as its equation
.
Which of the following is its slope?
A line on the coordinate plane has as its equation .
Which of the following is its slope?
Rewrite the equation in the slope-intercept form
, with
the slope, as follows:
Subtract
from both sides:



Multiply both sides by
, distributing on the right:





In the slope-intercept form, the coefficient of
is the slope
. This is
.
Rewrite the equation in the slope-intercept form , with
the slope, as follows:
Subtract from both sides:
Multiply both sides by , distributing on the right:
In the slope-intercept form, the coefficient of is the slope
. This is
.
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What is the slope of the following function? 
What is the slope of the following function?
To determine the slope, we will need the equation in slope-intercept form.

Divide by six on both sides.

Simplify the right side.

The answer is: 
To determine the slope, we will need the equation in slope-intercept form.
Divide by six on both sides.
Simplify the right side.
The answer is:
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Find the slope of the following equation:

Find the slope of the following equation:
If we look at the following equation

we can see it is written in slope-intercept form. Slope-intercept form is

where m is the slope and b is the y-intercept.
So, given the equation,

we can see -9 is the slope.
If we look at the following equation
we can see it is written in slope-intercept form. Slope-intercept form is
where m is the slope and b is the y-intercept.
So, given the equation,
we can see -9 is the slope.
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Find the slope of the following equation: 
Find the slope of the following equation:
The given equation is already in slope-intercept form.

The
represents the coefficient of the slope.
The answer is: 
The given equation is already in slope-intercept form.
The represents the coefficient of the slope.
The answer is:
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