Answer:
1) m=2/3
2) b=10
3) x-int:(-15, 0)
4) y-int: (0, 10)
Our equation is:
[tex]y=\frac{2}{3}x+10[/tex]
Step-by-step explanation:
To start, let’s find the equation of the line.
We can use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
Where m is the slope and (x₁, y₁) is a point.
So, let’s substitute 2/3 for m and (-3, 8) for (x₁, y₁). This yields:
[tex]y-8=\frac{2}{3}(x-(-3))[/tex]
Simplify:
[tex]y-8=\frac{2}{3}(x+3)[/tex]
Distribute:
[tex]y-8=\frac{2}{3}x+2[/tex]
Add 8 to both sides:
[tex]y=\frac{2}{3}x+10[/tex]
This is in slope intercept form: y=mx+b.
Therefore, our m is 2/3 and our b is 10.
To find the x-intercept, we will substitute 0 for y and solve for x. Therefore:
[tex]0=\frac{2}{3}x+10[/tex]
Subtract 10 from both sides:
[tex]-10=\frac{2}{3}x[/tex]
Multiply both sides by 3/2. So:
[tex]x=-10(\frac{3}{2})=-30/2=-15[/tex]
Therefore, the x-intercept is (-15, 0).
To find the y-intercept, we will substitute 0 for x and solve for y. Therefore:
[tex]y=\frac{2}{3}(0)+10=10[/tex]
So, the y-intercept is (0, 10).
We will also graph it. See the attachment. To graph by hand, we can start at the y-intercept and go up two for every three to the right. Or, we can go down two for every three to the left. This should yield the following graph:
