Question

Use the point-slope form linear equation given to complete the following problems.

y-3=3(x+1)

1. What is the slope of the given line?
Here's what I did:

y-3=3(x+1)
y-3+3=3x+3
y=3x+6
m=3

Correct so far?

2. What point does this line pass through, which is the basis of this equation?
I said (0,6)

3.Rewrite this equation in slope-intercept form.
I did this:
y=3x+6

4, What is the y-intercept of this line?
I said:
b=6

5. Rewrite the equation in standard form.
What I did:
Ax+By=C
3x=y=6

Is this correct?

6. What is the x-intercept of this line?
I'm not sure about this.

If you could check my work and help me complete the problems, I'd be so grateful.

Answer 1

You did well.
Some small errors

from y-3 = 3(x+1)
y-3 = 3x + 3
at this point you did:
y-3+3 = 3x+3
should have been
y-3+3 = 3x+3 + 3,
then
y = 3x + 6, which you have (so there were actually two errors here)

#2, looking at y-3 = 3(x+1)
and comparing it to the point-slope form of
y - y1 = m(x - x1)
our point was (-1,3)

#3, #4 are good

#5 should be:
3x - y = -6

If your equation is in standard form, the x-intercepts can be done in your head.
for the x-intercept, let y = 0
put your little pinkie finger over the y term (it is zero), then 3x = -6 ----> in your head, x = -2

for the y-intercept, let x=0
put your pinkie finger over the x term,
---> -y = -6 or y = 6 , which is also the b in y = 3x + 6