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.
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
Let's go through each problem one by one:
1. What is the slope of the given line?
You correctly identified the slope as 3. The coefficient of x in the equation represents the slope of the line.
2. What point does this line pass through, which is the basis of this equation?
To find the point through which the line passes, you need to look for the values of x and y in the equation. In this case, the equation is in the form (x, y) = (0, 6), which means the line passes through the point (0, 6).
3. Rewrite this equation in slope-intercept form.
The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept. Using the given equation, you correctly rewrote it as y = 3x + 6.
4. What is the y-intercept of this line?
The y-intercept is the point at which the line crosses the y-axis. In the equation y = 3x + 6, the constant term 6 is the y-intercept. So, you are correct that the y-intercept is 6.
5. Rewrite the equation in standard form.
The standard form of a linear equation is Ax + By = C, where A, B, and C are constants. To rewrite y = 3x + 6 in standard form, you need to rearrange the equation. Let's do that:
y = 3x + 6
-3x + y = 6
So, the correct standard form of the equation is -3x + y = 6.
6. What is the x-intercept of this line?
The x-intercept is the point at which the line crosses the x-axis. To find the x-intercept, set y = 0 in the equation y = 3x + 6 and solve for x:
0 = 3x + 6
-6 = 3x
-2 = x
Therefore, the x-intercept of the line is -2.
It seems you have a good understanding and answered most of the questions correctly. Just make sure to double-check your work for minor errors. Let me know if there is anything else I can help you with.