Other Lines
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GMAT Quantitative › Other Lines
Give the slope of the line of the equation:
Explanation
Rewrite in the slope-intercept form :
The slope is the coefficient of , which is
.
Fill in the circle with a number so that the graph of the resulting equation has slope :
None of the other responses is correct.
Explanation
Let be that missing coefficient. Then the equation can be rewritten as
Put the equation in slope-intercept form:
The coefficient of is the slope, so solve for
in the equation
Fill in the circle with a number so that the graph of the resulting equation has slope 4:
Explanation
Let be that missing coefficient. Then the equation can be rewritten as
Put the equation in slope-intercept form:
The coefficient of is the slope, so solve for
in the equation
Fill in the square and the circle with two numbers so that the line of resulting equation has slope :
in the square and
in the circle
in the square and
in the circle
in the square and
in the circle
in the square and
in the circle
None of the other responses is correct.
Explanation
Let and
be those missing numbers. Then the equation can be rewritten as
Put the equation in slope-intercept form:
The coefficient of is the slope, so solve for
in the equation
The number in the circle is irrelevant, so the correct choice is that goes in the square and
goes in the circle.
Examine these two equations.
Write a number in the box so that the lines of the two equations will have the same slope.
Explanation
Write the first equation in slope-intercept form:
The coefficient of , which here is
, is the slope of the line.
Now, let be the nuimber in the box, and rewrite the second equation as
Write in slope-intercept form:
The slope is , which is set to
:
Fill in the circle with a number so that the graph of the resulting equation is a horizontal line:
The graph cannot be a horizontal line no matter what number is written.
is the only number that works.
is the only number that works.
is the only number that works.
The graph is a horizontal line no matter what number is written.
Explanation
The equation of a horizontal line takes the form for some value of
. Regardless of what is written, the equation cannot take this form.
Fill in the circle with a number so that the graph of the resulting equation has slope 4:
It is impossible to do this.
Explanation
Once a number is filled in, the equation will be in slope-intercept form
,
so the coefficient of will be the slope of the line of the equation. Regardless of the number that is written in the circle, this coefficient, and the slope, will be 6, so the slope cannot be 4.
Determine the equation of a line that has the points and
?
Explanation
The equation for a line in standard form is written as follows:
Where is the slope and
is the y intercept. We start by calculating the slope between the two given points using the following formula:
Now we can plug either of the given points into the formula for a line with the calculated slope and solve for the y intercept:
We now have the slope and the y intercept of the line, which is all we need to write its equation in standard form:
What is the slope of the line that contains and
?
Explanation
The slope formula is:
Give the slope of the line with the equation .
Explanation
Rewrite in slope-intercept form:
The slope is the coefficient of , which is
.