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!