Answer:
y = 4/5(x) - 6
Explanation:
The generic form of a slope/intercept equation is:
y = mx + b
where m is the slope and b is the intercept (with the y-axis, or what y is when x=0).
"Slope" is the change in y divided by the change in x. Or the "rise" over the "run."
It helps to visualize these if you graph them out, so I've attached a graph of the two points. I also added a line that passes through and beyond the two points, because it's helpful to see where the function crosses each axis.
So what's the change in y between the two given points? It's easy to see on the graph, it's 4 units, or you can do -2 - (-6) = 4.
Be careful with signs! And the standard is that if y gets bigger from the left-most point to the right-most point (that is, if the line slopes up and to the right), that's a positive rise.
What's the change in x? You can see from the graph that it's 5 units. And since x got bigger from the 1st point to the 2nd, it's a positive change in x. Or you can take the x=5 in the second point and subtract x=0 in the first point: same five units, and it's positive.
So the slope, m = rise/run = 4/5
So we can plug that previously-unknown value into the standard equation and get:
y = 4/5(x) + b
So now we have to find the intercept, or: What is y when x=0?
You can see in that equation that if x=0 then that x term goes away and we're left with y = b, which is the thing we're trying to find.
Now just use one of the given points and substitute for x and y! How cool is that?
If we use (0,-6), then substituting:
-6 = 4/5(0) + b --> -6 = 0 + b --> -6 = b
Or turn it around for the more-normal: b = -6
Then put it all together, and:
y = 4/5(x) - 6
But it's always good to check our work, and we have another known point on the line we can use to check. So substitute in (5,-2) and see if it satisfies our equation:
-2 = 4/5(5) - 6 = 4 - 6 = -2
Both sides match, so the equation works for the 2nd point also. (We don't need to check with the first point, because we used it already to derive b. But you could if you want, it'll work.)