How to graph a line - ACT Math
Card 0 of 8
Refer to the above red line. A line is drawn perpendicular to that line, and with the same 
-intercept. Give the equation of that line in slope-intercept form.
Refer to the above red line. A line is drawn perpendicular to that line, and with the same
First, we need to find the slope of the above line.
The slope of a line. given two points 
can be calculated using the slope formula
Set 
:
The slope of a line perpendicular to it has as its slope the opposite of the reciprocal of 2, which would be 
. Since we want this line to have the same 
-intercept as the first line, which is the point 
, we can substitute 
and 
in the slope-intercept form:
First, we need to find the slope of the above line.
The slope of a line. given two points
Set
The slope of a line perpendicular to it has as its slope the opposite of the reciprocal of 2, which would be
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The equation 
represents a line. This line does NOT pass through which of the four quadrants?
The equation
Plug in 
for 
to find a point on the line:
Thus, 
is a point on the line.
Plug in 
for 
to find a second point on the line:
is another point on the line.
Now we know that the line passes through the points 
and 
.
A quick sketch of the two points reveals that the line passes through all but the third quadrant.
Plug in
Thus,
Plug in
Now we know that the line passes through the points
A quick sketch of the two points reveals that the line passes through all but the third quadrant.
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What is the distance between (7, 13) and (1, 5)?
What is the distance between (7, 13) and (1, 5)?
The distance formula is given by d = square root \[(x2 – x1)2 + (y2 – y1)2\]. Let point 2 be (7,13) and point 1 be (1,5). Substitute the values and solve.
The distance formula is given by d = square root \[(x2 – x1)2 + (y2 – y1)2\]. Let point 2 be (7,13) and point 1 be (1,5). Substitute the values and solve.
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What is the midpoint between 
and 
?
What is the midpoint between
The x-coordinate for the midpoint is given by taking the arithmetic average (mean) of the x-coordinates of the two end points. So the x-coordinate of the midpoint is given by 
The same procedure is used for the y-coordinates. So the y-coordinate of the midpoint is given by 
Thus the midpoint is given by the ordered pair 
The x-coordinate for the midpoint is given by taking the arithmetic average (mean) of the x-coordinates of the two end points. So the x-coordinate of the midpoint is given by
The same procedure is used for the y-coordinates. So the y-coordinate of the midpoint is given by
Thus the midpoint is given by the ordered pair
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What is the slope of this line?
What is the slope of this line?
The slope is found using the formula 
.
We know that the line contains the points (3,0) and (0,6). Using these points in the above equation allows us to calculate the slope.
The slope is found using the formula
We know that the line contains the points (3,0) and (0,6). Using these points in the above equation allows us to calculate the slope.
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If the graph has an equation of 
, what is the value of 
?
If the graph has an equation of
is the 
-intercept and equals 
. 
can be solved for by substituting 
in the equation for 
, which yields 
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What is the amplitude of the function if the marks on the y-axis are 1 and -1, respectively?
What is the amplitude of the function if the marks on the y-axis are 1 and -1, respectively?
The amplitude is half the measure from a trough to a peak.
The amplitude is half the measure from a trough to a peak.
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Refer to the above diagram. If the red line passes through the point 
, what is the value of 
?
Refer to the above diagram. If the red line passes through the point
One way to answer this is to first find the equation of the line.
The slope of a line. given two points 
can be calculated using the slope formula
Set 
:
The line has slope 3 and 
-intercept 
, so we can substitute 
in the slope-intercept form:
Now substitute 4 for 
and 
for 
and solve for 
:
One way to answer this is to first find the equation of the line.
The slope of a line. given two points
Set
The line has slope 3 and
Now substitute 4 for
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