Math I Don't Get?

Question

My little cousin is in ninth grade and is taking algebra 1. He asked me for help on these questions, but I, not being a math person by any stretch, don't get them. Could someone tell me the answers to these?

1. Write an equation of the line that is parallel to the given line
y = x + 3 and the given point (5,0).

2. Write an equation of the line that is parallel to the given line
y = 2x + 3 and the given point (-4,1).

3. Write an equation in slope-intercept form of the line that passes through the points (-4,2) and (1,-1).

4. Write an equation in slope-intercept form of the line that passes through the points (-2,-1) and (3,5).

Answer 1

1. The general form for a line is y = mx+b -- where m is the slope and b is the intercept. The equation y = x+3 has a slope of one and an intercept of 3. Since you want a new equation that is parallel to it -- it will also have a slope of one. Since it has to go through (1,5), b = 5. Your equation is:

y = x+5

2. Again, since it is parallel -- it has to have the same slope as y = 2x+3. -- which is 2, Therefore, it must have the form

y = 2x+b. To find b, plug in (-4) for x and (1) for y --

1 = 2*(-4)+b
1 = -8 + b
b = 9

3. Here you need to find the slope of the line that goes through those two points. It is the difference of the Y values divided by the difference of the x values. That is
(2-(-1)/((-3)-1) = 3/(-4) = -3/4 -- so the slope is -3/4

Now go back to the earlier equation I gave you -- y = mx+b. m is the -3/4 -- so you get:

y = -(3/4)*x+b

Now plug in one of the points to solve for b -- let x = -4 and y = 2, we get:

2 = -(3/4)*(-4)+b
2 = 3+b
b = -1

Do #4 the same way.

Answer 2

1.)y=x+5