Question

SOMEONE PLEASE HELP ANSWER MY QUESTIONS!!!!!!!!!!!!

1) A line has a slope of 5 and passes through the points (4, 3) and (2, y).

What is the value of y?

y = _____



2) A line passes through the origin and has a slope of −32. Through which quadrants does the line pass? (Use Roman numerals: I, II, III, IV; write your answer in the form of: II and III)

Answer 1

1)

`y=mx+b`
where m is the slope

We know the slope is 5 and the line passes through the point (4,3).


`m=5 \\ (4,3) \\ x=4 \\ y=3 \\ \\ 3=5 * 4 + b \\ 3=20 + b \\ b=3-20 \\ b=-17`

The equation of the line is:

`y=5m-17`

Now the second point:

`(2,y) \\ x=2 \\ y \\ \\ y=5 * 2 -17 \\ y=10-17 \\ y=-7`

The answer:
The value of y is -7.

2)
The line passes through the origin, or the point (0,0), and has a slope of -32.
The slope is negative so the line goes down from left to right.
It crosses both x and y axes in the point (0,0).
Therefore, it only passes through II and IV quadrant.

You can also find the equation of the line, find one more point and draw it.

`y=mx+b \\ \\ m=-32 \\ (0,0) \\ x=0 \\ y=0 \\ \\ 0=-32 * 0 + b \\ b=0 \\ \\ y=-32x`

Find the y-coordinate of the point for example (1,y).

`(1,y) \\ x=1 \\ y \\ \\ y=-32 * 1 \\ y=-32`

The line passes through the points (0,0) and (1,-32). Now you can draw it (see the attachment).

The answer:
The line passes through quadrants II and IV.