Answer:
[tex]y=-\frac{1}{4}x+4[/tex]
Step-by-step explanation:
Ok, so the slope-intercept form is generally expressed as: [tex]y=mx+b[/tex]
y-intercept:
Let's start by explaining why the "b" value represents the y-intercept. So I attached a graph to make this a bit more understandable, but the gist is that anywhere on the y-axis, is going to have x=0, any point on the y-axis can generally be expressed as (0, y).
This means, if we want to find the y-intercept, using the slope intercept form, we simply plug in 0 as x, since that's what x will always be equal to at the y-intercept.
We get the following equation: [tex]y=m(0) + b[/tex], and since anything times zero is just zero, we can simplify this to: [tex]y=b[/tex], meaning the y-intercept will be the "b" value in any slope-intercept form equation.
The slope:
By definition the slope is just how much the y-value changes as x increase by one. Whenever we increase the x-value by one, in the equation y=mx+b, we have one more "m", or the value is increasing by m.
Let's look at an example:
[tex]y=m(1) +b\implies m+b[/tex]
[tex]y=m(2) + b \implies m + m + b[/tex]
[tex]y = m(3) + b \implies m + m + m +b[/tex]
See how each time we increase the value "x" by one, the value of "y" increases by m. So by definition "m" is the value of the slope.
So putting this all together with your example, we get the following equation:
[tex]y=-\frac{1}{4}x+4[/tex]
