First we convert into slope-intercept form | y = mx + b
[tex]-3y=-3-x[/tex]
Move x to another side and subtract. (Whenever you move to another side, the sign/operator will be opposite. From plus to minus and from multiply to divide.)
Then move -3 to divide (-3-x)
[tex]y=\frac{-3-x}{-3}[/tex]
Separate - [tex]y=\frac{-3}{-3}-\frac{x}{-3}[/tex]
| Negative dividing Negative equal positive |
[tex]y=\frac{3}{3}-(-\frac{x}{3})[/tex] | When the denominator is negative, we can pull out from the denominator and convert into the middle of fraction. |
| Negative multiplying Negative equal positive |
[tex]y=1+\frac{x}{3}[/tex]
This is not fully slope-intercept form yet. We swap the position of 1 and x/3
[tex]y=\frac{x}{3}+1[/tex]
There we go. The slope-intercept form.
Now our job is to find the x-intercept and y-intercept. First, know what m and b represents in the equation y = mx + b first.
From y = mx + b | m represents slope | b represents the y-intercept. |
Our equation is [tex]y=\frac{x}{3}+1[/tex]
Our m or slope is 1/3 and our y-intercept is 1. So we don't need to find the y-intercept because we've already found it.
Now move to finding x-intercept.
Substitute y as we get -
[tex]0=\frac{x}{3}+1[/tex]
Now whenever there is a denominator, multiply the whole equation by the denominator itself. As our denominator in this equation is 3, so we multiply all whole equation by 3.
[tex]0(3)=\frac{x}{3}(3)+1(3)\\0=x+3 \\x=-3[/tex]
Our x-intercept is x = -3 and y-intercept is y = 1.
Check the graph out. Our answers can be only A and B considering the slope is positive. C and D choices have negative slope (m < 0).
However, the value of slope also affects the graph. If the slope has a lot of value, then the graph will head to y-axis.
But if the slope has a little value then the graph will head to x-axis instead.
After all, when converting to the slope-intercept form. We don't need to find the x-intercept right away, just one glance at the graph along with the equation and we are able to answer it.
Thus, the answer is B choice.
I know it is a long, boring explanation. But providing a quality answer is what I'm trying to do. I may not be able to explain that good or whatever. But with an explanation, I hope it will benefit you someday, after all. An explanation can help you in a test. Thanks for reading and I hope this helps you.
