1. Write an equation in slope- intercept form of the line that passes through the given point and is parallel to the graph of the given equation. (2,-2);y=-x-2
A. y=-2x
B. y=2x
C. y=1/2x
D. y=-x***
2. Write an equation in slope- intercept form of the line that passes through the given point and is parallel to the graph of the given equation. (2,-1);y=-3/2x-6
A. y=-3/2x+1
B. y=-3/2x-1
C. y=-3/2x+2***
D. y=-3/2x+4
3. Write an equation in slope- intercept form of the line that passes through the given point and is parallel to the graph of the given equation. (4,2);x=-3
A. y=2
B. y=2x+4
C. y=4x
D. y=4***
4. Write an equation in slope- intercept form of the line that passes through the given point and is perpendicular to the graph of the given equation. (-2,3);y=1/2x-1
A. y=1/2x+1
B. y=-2x-1***
C. y=1/2x-1
D. y=-1/2x-1
5. Write an equation in slope- intercept form of the line that passes through the given point and is perpendicular to the graph of the given equation. (5,0);y+1=2(x-3)
A. y=-1/2x+5
B. y=2x-5
C. y=1/2x-2
D. y=-1/2x+5/2***
Can these be Checked?
Eliminate all the answers that aren't parallel, then eliminate the answers which don't pass through the given point for X,Y
So for the graph to be "PARALLEL" it must have the exact same slope. The "slope" is represented by the value in front of the 'X'. This is very useful information. If we have y=2x + 5, a PARALLEL line might be y=2x+3.
So you can look at something like question 1 and see that in all the possible answers, only option C has the same slope as the slope (-1) in y=-x-2.
Now, onto question 2 where we'll need to eliminate answers based on whether or not they pass through the given point.
We know that the correct answer to question 2 will pass through the point 2,-1 (that's x=2, y=-1). So we can plug in '2' for X into each answer's equation and see which equation returns -1 for our y value. The only one which does in answer 2 is C.
By the way, for the question asked in question 3, I think you meant to write y=-3 instead of x=-3
Note that in my response, I made a typo in this line:
"So you can look at something like question 1 and see that in all the possible answers, only option C has the same slope as the slope (-1) in y=-x-2. "
I meant to write option D
Oh, put the "Can these be checked" in the top of the post next time xD
Your answer to question 3 is incorrect.
Actually all my answers where correct you where a little late.
Yes, I can help you check the answers to these questions. Let's go through each question and equation one by one.
1. The given equation is y = -x - 2. To find an equation that is parallel to this line, we need to use the fact that parallel lines have the same slope. Since the slope of the given line is -1, the slope of the line we're looking for will also be -1.
Now we have the slope (-1) and the given point (2, -2). We can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
Plugging in the values, we get:
y = -1x + b
-2 = -1(2) + b
-2 = -2 + b
b = 0
Therefore, the equation in slope-intercept form for the line that passes through (2,-2) and is parallel to the given equation is y = -x.
The correct answer is D. y = -x.
2. The given equation is y = -3/2x - 6. Similar to the previous question, we need to find an equation with the same slope since the line is parallel. The slope here is -3/2.
Using the slope-intercept form, y = mx + b, we plug in the given point (2,-1):
-1 = -3/2(2) + b
-1 = -3 + b
b = 2
So the equation in slope-intercept form for the line that passes through (2,-1) and is parallel to the given equation is y = -3/2x + 2.
The correct answer is C. y = -3/2x + 2.
3. The given equation is x = -3. This equation represents a vertical line parallel to the y-axis. To find a line parallel to it, we need to maintain the equation with the same value of x and adjust the y-intercept.
Since the line passes through the point (4,2), the value of x remains 4. Therefore, the equation in slope-intercept form is y = 2.
The correct answer is A. y = 2.
4. The given equation is y = 1/2x - 1. To find a line perpendicular to it, we need to change the sign of the slope and take its reciprocal. The reciprocal of 1/2 is 2/1 or simply 2. The new slope is -2.
Now, using the slope-intercept form, y = mx + b, we plug in the point (-2,3):
3 = -2(-2) + b
3 = 4 + b
b = -1
So the equation in slope-intercept form for the line that passes through (-2,3) and is perpendicular to the given equation is y = -2x - 1.
The correct answer is B. y = -2x - 1.
5. The given equation is y + 1 = 2(x - 3). We first need to rewrite it in slope-intercept form. Expanding the equation, we have:
y + 1 = 2x - 6
y = 2x - 7
The slope of the given equation is 2. Since we want a line perpendicular to it, the new slope is the negative reciprocal of 2, which is -1/2.
Using the given point (5,0), we can write the equation in slope-intercept form:
0 = -1/2(5) + b
0 = -5/2 + b
b = 5/2
Therefore, the equation in slope-intercept form for the line that passes through (5,0) and is perpendicular to the given equation is y = -1/2x + 5/2.
The correct answer is D. y = -1/2x + 5/2.
I have checked the answers for you. If you have any more questions, feel free to ask!