Two equations have an additive relationship. Name a point that will not be on either line.(1 point)

Question

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Answer 1

(0,0)

Answer 2

The two equations y=2x+10 and y=3x+15 have an additive relationship. While they do not share the same slope or y -intercept, they do have a common x -intercept. Identify that common point.(1 point)

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Answer 3

To find the common x-intercept, we need to set y equal to 0 in both equations and solve for x.

For the first equation y = 2x + 10:
0 = 2x + 10
-10 = 2x
x = -5

For the second equation y = 3x + 15:
0 = 3x + 15
-15 = 3x
x = -5

Therefore, the common x-intercept for both equations is -5.

The common point is: (-5, 0)

Answer 4

Compare the equations −12x+y=8 and 12y=14x−4 . Identify the true statement.(1 point) Responses The equations have no common characteristics. The equations have no common characteristics. The equations have the same y-intercept, or initial value. The equations have the same y -intercept, or initial value. The equations have the same slope and y-intercept. The equations have the same slope and y -intercept. The equations have the same slopes and are parallel lines.

Answer 5

The true statement is: The equations have the same slope and y-intercept.

Answer 6

Given the equation 6x−3y=12, find the value for a in the equation ax−2y=10 that will produce perpendicular lines.(1 point) Responses −1 negative 1 −4 negative 4 4

Answer 7

To find the value of "a" that will produce perpendicular lines, we need to compare the slope of the given equation with the slope of the equation ax - 2y = 10.

The given equation is 6x - 3y = 12.
To find its slope, let's rewrite it in slope-intercept form (y = mx + b) by solving for y:
6x - 3y = 12
-3y = -6x + 12
y = 2x - 4

The slope of the given equation is 2.

Now, let's compare it to the equation ax - 2y = 10.
To find the slope of this equation, we need to rewrite it in slope-intercept form:
ax - 2y = 10
-2y = -ax + 10
y = (a/2)x - 5

For the lines to be perpendicular, the slopes must be negative reciprocals of each other. In other words, if the slope of one line is m, the slope of the other line is -1/m.

Since the slope of the given equation is 2, the slope of the equation ax - 2y = 10 should be -1/2 for it to be perpendicular.

Therefore, a = -1.

The value of "a" that will produce perpendicular lines is -1.

Answer 8

Identify the true statement comparing equations x+y=−1 and x−y=−1.(1 point) Responses The equations have the same y-intercept. The equations have the same y -intercept. The equations have the same slope. The equations have the same slope. The equations have the same slope and the same y-intercept. The equations have the same slope and the same y -intercept. The equations have neither the same slope nor the same y-intercept.

Answer 9

The true statement is: The equations have neither the same slope nor the same y-intercept.

Answer 10

Which of the following is the correct comparison of the linear additive relationships in the graph? (1 point) Responses The lines have different slopes, so they are parallel. The lines have different slopes, so they are parallel. The lines have the same slope but different y-intercepts, so they are parallel. The lines have the same slope but different y -intercepts, so they are parallel. The lines appear to be parallel, but without a ruler, it cannot be determined. The lines appear to be parallel, but without a ruler, it cannot be determined. The lines both have negative slopes, so they are parallel.

Answer 11

The lines have different slopes, so they are parallel.