DSQ: Calculating the equation of a line - GMAT Quantitative Reasoning
Card 0 of 5
Find the equation of linear function 
given the following statements.
I) 
II) 
intercepts the x-axis at 9.
Find the equation of linear function
I)
II)
To find the equation of a linear function, we need some combination of slope and a point.
Statement I gives us a clue to find the slope of the desired function. It must be the opposite reciprocal of the slope of 
. This makes the slope of 
equal to 
Statement II gives us a point on our desired function, 
.
Using slope-intercept form, we get the following:
So our equation is as follows
To find the equation of a linear function, we need some combination of slope and a point.
Statement I gives us a clue to find the slope of the desired function. It must be the opposite reciprocal of the slope of
Statement II gives us a point on our desired function,
Using slope-intercept form, we get the following:
So our equation is as follows
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Find the equation for linear function 
.
I) 
and 
II) 
Find the equation for linear function
I)
II)
Find the equation for linear function p(x)
I) 
and 
II) 
To begin:
I) Tells us that p(x) must have a slope of 16
II) Tells us a point on p(x). Plug it in and solve for b:
Find the equation for linear function p(x)
I)
II)
To begin:
I) Tells us that p(x) must have a slope of 16
II) Tells us a point on p(x). Plug it in and solve for b:
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There are two lines in the xy-coordinate plane, a and b, both with positive slopes. Is the slope of a greater than the slope of b?
1)The square of the x-intercept of a is greater than the square of the x-intercept of b.
- Lines a and b have an intersection at
There are two lines in the xy-coordinate plane, a and b, both with positive slopes. Is the slope of a greater than the slope of b?
1)The square of the x-intercept of a is greater than the square of the x-intercept of b.
- Lines a and b have an intersection at
Given that the square of a negative is still positive, it is possible for a to have an x-intercept that is negative, while still having a positive slope. The example above shows how the square of the x-intercept for line a could be greater, while having still giving line a a slope that is less than that of b.
Given that the square of a negative is still positive, it is possible for a to have an x-intercept that is negative, while still having a positive slope. The example above shows how the square of the x-intercept for line a could be greater, while having still giving line a a slope that is less than that of b.
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Line j passes through the point 
. What is the equation of line j?
-
Line j is perpindicular to the line defined by 
-
Line j has an x-intercept of 
Line j passes through the point
-
Line j is perpindicular to the line defined by
-
Line j has an x-intercept of
Either statement is sufficient.
Line j, as a line, has an equation of the form 
Statement 1 gives the equation of a perpindicular line, so the slopes of the two lines are negative reciprocals of each other:
Statement 2 allows the slope to be found using rise over run:
Then, since the x-intercept is known:
Either statement is sufficient.
Line j, as a line, has an equation of the form
Statement 1 gives the equation of a perpindicular line, so the slopes of the two lines are negative reciprocals of each other:
Statement 2 allows the slope to be found using rise over run:
Then, since the x-intercept is known:
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Give the equation of a line.
Statement 1: The line interects the graph of the equation 
on the 
-axis.
Statement 2: The line interects the graph of the equation 
on the 
-axis.
Give the equation of a line.
Statement 1: The line interects the graph of the equation
Statement 2: The line interects the graph of the equation
Assume both statements to be true. Then the line shares its 
- and 
-intercepts with the graph of 
, which is a parabola. The common 
-intercept can be found by setting 
and solving for 
:
,
making the 
-intercept of the parabola, and that of the line, 
.
The common 
-intercept can be found by setting 
and solving for 
:
, in which case 
, or
, in which case 
,
The parabola therefore has two 
-intercepts, 
and 
, so it is not clear which one is the 
-intercept of the line. Therefore, the equation of the line is also unclear.
Assume both statements to be true. Then the line shares its
making the
The common
The parabola therefore has two
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