Card 0 of 800
Give the equation of the line through and
.
First, find the slope:
Apply the point-slope formula:
Rewriting in standard form:
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A line can be represented by . What is the slope of the line that is perpendicular to it?
You will first solve for Y, to get the equation in form.
represents the slope of the line, which would be
.
A perpendicular line's slope would be the negative reciprocal of that value, which is .
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Examine the above diagram. What is ?
Use the properties of angle addition:
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Give the equation of a line that passes through the point and has an undefined slope.
A line with an undefined slope has equation for some number
; since this line passes through a point with
-coordinate 4, then this line must have equation
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Give the equation of a line that passes through the point and has slope 1.
We can use the point slope form of a line, substituting .
or
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Find the equation the line goes through the points and
.
First, find the slope of the line.
Now, because the problem tells us that the line goes through , our y-intercept must be
.
Putting the pieces together, we get the following equation:
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A line passes through the points and
. Find the equation of this line.
To find the equation of a line, we need to first find the slope.
Now, our equation for the line looks like the following:
To find the y-intercept, plug in one of the given points and solve for . Using
, we get the following equation:
Solve for .
Now, plug the value for into the equation.
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What is the equation of a line that passes through the points and
?
First, we need to find the slope of the line.
Next, find the -intercept. To find the
-intercept, plug in the values of one point into the equation
, where
is the slope that we just found and
is the
-intercept.
Solve for .
Now, put the slope and -intercept together to get
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Are the following two equations parallel?
When two lines are parallal, they must have the same slope.
Look at the equations when they are in slope-intercept form, where b represents the slope.
We must first reduce the second equation since all of the constants are divisible by .
This leaves us with . Since both equations have a slope of
, they are parallel.
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Reduce the following expression:
For this expression, you must take each variable and deal with them separately.
First divide you two constants .
Then you move onto and when you divide like exponents you must subtract the exponents leaving you with
.
is left by itself since it is already in a natural position.
Whenever you have a negative exponential term, you must it in the denominator.
This leaves the expression of .
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For the line
Which one of these coordinates can be found on the line?
To test the coordinates, plug the x-coordinate into the line equation and solve for y.
y = 1/3x -7
Test (3,-6)
y = 1/3(3) – 7 = 1 – 7 = -6 YES!
Test (3,7)
y = 1/3(3) – 7 = 1 – 7 = -6 NO
Test (6,-12)
y = 1/3(6) – 7 = 2 – 7 = -5 NO
Test (6,5)
y = 1/3(6) – 7 = 2 – 7 = -5 NO
Test (9,5)
y = 1/3(9) – 7 = 3 – 7 = -4 NO
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Consider the lines described by the following two equations:
4y = 3x2
3y = 4x2
Find the vertical distance between the two lines at the points where x = 6.
Since the vertical coordinates of each point are given by y, solve each equation for y and plug in 6 for x, as follows:
Taking the difference of the resulting y -values give the vertical distance between the points (6,27) and (6,48), which is 21.
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Solve the following system of equations:
–2x + 3y = 10
2x + 5y = 6
Since we have –2x and +2x in the equations, it makes sense to add the equations together to give 8y = 16 yielding y = 2. Then we substitute y = 2 into one of the original equations to get x = –2. So the solution to the system of equations is (–2, 2)
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Which of the following sets of coordinates are on the line ?
when plugged in for
and
make the linear equation true, therefore those coordinates fall on that line.
Because this equation is true, the point must lie on the line. The other given answer choices do not result in true equalities.
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Which of the following points can be found on the line ?
We are looking for an ordered pair that makes the given equation true. To solve, plug in the various answer choices to find the true equality.
Because this equality is true, we can conclude that the point lies on this line. None of the other given answer options will result in a true equality.
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Which of the following points is on both the line
and the line
In the multiple choice format, you can just plug in these points to see which satisfies both equations. and
work for the first but not the second, and
and
work for the second but not the first. Only
works for both.
Alternatively (or if you were in a non-multiple choice scenario), you could set the equations equal to each other and solve for one of the variables. So, for instance,
and
so
Now you can solve and get . Plug this back into either of the original equations and get
.
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A line has the equation . Which of the following points lies on the line?
Plug the x-coordinate of an answer choice into the equation to see if the y-coordinate matches with what comes out of the equation.
For ,
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Which of the following points lies on the line with equation ?
To find which point lies on the line, plug in the x-coordinate value of an answer choice into the equation. If the y-coordinate value that comes out of the equation matches that of the answer choice, then the point is on the line.
For ,
So then, lies on the line.
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Which of the following points is on the line with the equation ?
To find if a point is on the line, plug in the x-coordinate of the answer choice into the given equation. If the resulting value for the y-coordinate matches that of the answer choice, then that point is on the line.
For ,
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Which of the following points lies on the line with the equation ?
To find if a point is on the line, plug in the x-coordinate of the answer choice into the given equation. If the resulting value for the y-coordinate matches that of the answer choice, then that point is on the line.
For ,
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