I need help with two Algebra problems!?

Question

They are:

Write the equation of the line that passes through (0,2) and (4,-1) in standard AND slope intercept form.

The second one is the same but the coordinates are (-1,3) and (6,-2)

Answer 1

The easiest way to do these is to first find the slope, then use the point-slope form.  After that, you can massage them algebraically at will.

Slope formula:  m = (y2 - y1)/(x2 - x1)

For your first problem, m = (-1 - 2)/(4 - 0) = -3/4

Point-slope:  y - y1 = m(x - x1)

It doesn't matter which point you use.  Since I like 0, let's use the first:

y - 2 = (-3/4)(x - 0)

y - 2 = (-3/4)x

Now:  slope-intercept form, just solve for y:

y = (-3/4)x + 2

In standard form, get x and y on one side, leave the constant on the other, and (if possible) get rid of fractions:

y = (-3/4)x + 2

(3/4)x + y = 2

3x + 4y = 8

This process will work on the other problem, too.  Go, now, and do thou likewise.

Answer 2

slope intercept is

Y=mx+b

in this case.. it would be

Y=m(2)-1

the second one is

Y=m(1)-2(+1)