1. Write an equation in slope-intercept form for the line that passes through (5,0) and is perpendicular to the line given by y = -5/2x + 6.

A: m = 2/5

y = mx + b

0 = (2/5)(5) + b

0 = 2 + b
b = -2

y = 2x/5 -2?

2. Write an equation in slope-intercept form for the line that passes through (0, 0) and is parallel to the line given by y = -6/7x + 1.

A: ?

Identify which lines are parallel.

3. y = -2x; y = 2x + 1; y = 2x; y = 2(x + 5)

A: All of the above.

4. -3y = x; y = -1/3x + 1; y = -3x; y + 2 = x + 4

A: y = -1/3x + 1; y = -3x?

5. y = -3x + 2; y = 1/2x - 1; -x + 2y = 17; 3x + y = 27

A: y = -3x + 2; 3x + y = 27?

Can someone please help me?

#1 ok

you can avoid solving for b by using the point-slope form:

y-0 = 2/5 (x-5)

#2 how could you get #1 and not get #2?
m = -6/7
point-slope form:
y-0 = -6/7 (x-0)
y = -6x/7
all this means is that b=0

#3 1st has slope -2
the others all have slope 2

#4 only the 1st two.
The slopes are -1/3, -1/3 -3,1

#5 almost. the slopes are
-3, 1/2, 1/2, -3
so, your answer is correct, but there are 2 pairs of parallel lines.

To clarify:

3. Incorrect; y = 2x + 1; y = 2x; y = 2(x + 5)

4. Incorrect; -3y = x; y = -1/3x + 1

5. I don't quite understand what you said.

I'm just saying that the two you picked are parallel, but so are the other two. Don't know how the question is structured, and how you can answer, but unless there's a typo, there are two possible choices.

1. First, we need to find the slope of the given line. The equation y = -5/2x + 6 is already in slope-intercept form y = mx + b, where m is the slope. In this case, the slope is -5/2.

To find the slope of a line perpendicular to a given line, we can take the negative reciprocal of the slope. The negative reciprocal of -5/2 is 2/5.

Now, we have the slope (m = 2/5) and a point (5, 0) that the line passes through. We can use the point-slope form of the equation:

y - y₁ = m(x - x₁),

where (x₁, y₁) are the coordinates of the given point and m is the slope.

Substituting the values, we have:

y - 0 = (2/5)(x - 5),

y = 2/5(x - 5),

Simplifying,

y = 2/5x - 2.

So, the equation in slope-intercept form for the line that passes through (5, 0) and is perpendicular to the given line is y = 2/5x - 2.

2. To find an equation in slope-intercept form for a line that is parallel to a given line, we need to use the same slope as the given line.

The given line, y = -6/7x + 1, is already in slope-intercept form, where the slope (m) is -6/7.

Now, we have the slope (-6/7) and a point (0, 0) that the line passes through. We can use the point-slope form of the equation to find the equation for the parallel line:

y - y₁ = m(x - x₁),

where (x₁, y₁) are the coordinates of the point and m is the slope.

Substituting the values, we get:

y - 0 = (-6/7)(x - 0),

y = -6/7x.

So, the equation in slope-intercept form for the line that passes through (0, 0) and is parallel to the given line is y = -6/7x.