SSAT Upper Level Quantitative › Coordinate Geometry
Which of the following lines is parallel to the line ?
For two lines to be parallel, their slopes must be the same. Thus, the line that is parallel to the given one must also have a slope of .
Find the equation of a line that goes through the point and is parallel to the line with the equation
.
For lines to be parallel, they must have the same slope. The slope of the line we are looking for then must be .
The point that's given in the equation is also the y-intercept.
Using these two pieces of information, we know that the equation for the line must be
Which of the following lines is parallel with the line ?
Parallel lines have the same slope. The slope of a line in slope-intercept form is the value of
. So, the slope of the line
is
. That means that for the two lines to be parallel, the slope of the second line must also be
.
There is a line defined by the equation below:
There is a second line that passes through the point and is parallel to the line given above. What is the equation of this second line?
Parallel lines have the same slope. Solve for the slope in the first line by converting the equation to slope-intercept form.
3x + 4y = 12
4y = _–_3x + 12
y = –(3/4)x + 3
slope = _–_3/4
We know that the second line will also have a slope of _–_3/4, and we are given the point (1,2). We can set up an equation in slope-intercept form and use these values to solve for the y-intercept.
y = mx + b
2 = _–_3/4(1) + b
2 = _–_3/4 + b
b = 2 + 3/4 = 2.75
Plug the y-intercept back into the equation to get our final answer.
y = –(3/4)x + 2.75
Which of the following lines is parallel to the line ?
For two lines to be parallel, their slopes must be the same. Thus, the line that is parallel to the given one must also have a slope of .
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.
36
21
12
44
48
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.
What equation is graphed in the above figure?
The greatest integer function, or floor function, , pairs each value of
with the greatest integer less than or equal to
. Its graph is below.
The given graph is the above graph shifted downward four units. The graph of any function shifted downward four units is
, so the given graph corresponds to equation
.
What line is perpendicular to and passes through
?
Convert the given equation to slope-intercept form.
The slope of this line is . The slope of the line perpendicular to this one will have a slope equal to the negative reciprocal.
The perpendicular slope is .
Plug the new slope and the given point into the slope-intercept form to find the y-intercept.
So the equation of the perpendicular line is .
There is a line defined by the equation below:
There is a second line that passes through the point and is parallel to the line given above. What is the equation of this second line?
Parallel lines have the same slope. Solve for the slope in the first line by converting the equation to slope-intercept form.
3x + 4y = 12
4y = _–_3x + 12
y = –(3/4)x + 3
slope = _–_3/4
We know that the second line will also have a slope of _–_3/4, and we are given the point (1,2). We can set up an equation in slope-intercept form and use these values to solve for the y-intercept.
y = mx + b
2 = _–_3/4(1) + b
2 = _–_3/4 + b
b = 2 + 3/4 = 2.75
Plug the y-intercept back into the equation to get our final answer.
y = –(3/4)x + 2.75
Find the equation of a line that goes through the point and is parallel to the line with the equation
.
For lines to be parallel, they must have the same slope. The slope of the line we are looking for then must be .
The point that's given in the equation is also the y-intercept.
Using these two pieces of information, we know that the equation for the line must be