You can solve this by making a table of values. However, I will solve this more mathematically (sorta).
The -5 part says that the y-intercept of this line is -5. The y-intercept is the point at which a line crosses the y axis. Therefore, x is always 0 for the y intercept.
The 1/4x is implying that the slope or the gradient (same thing) of this line is 1/4. Therefore, (Rise)/(Run)=1/4. (Rise)/(Run) can be expanded to (y_2-y_1)/(x_2-x_1).
Since we already know that the point {0,-5} lies on this line, let's substitute x_2 for 0 and y_2 for -5.
(-5-y_1)/(0-x_1)=1/4
Now, if you choose a point for x_1, you can simply work out y_1. For example, let's say I chose 4.
(-5-y_1)/(0-4)=1/4
=(-5-y_1)/-4=1/4
Now, what makes 1/4 when divided by -4? The answer is -1.
Therefore, we need -1 on the numerator. We already have -5, and y_1 is negative, so the number -4 fits. So the coordinates for the 2nd point is {4,-4}
(-5--4)/-4=1/4
=(-1)/-4=1/4
Now, with the points we have, {0,-5} and {4,-4}, we can graph this by plotting the points and joining them.
You should get this graph{y=1/4x-5 [-10, 10, -5, 5]}
Sorry for this long answer, but with enough practice, you really don't need to go through all of the steps. You develop a muscle memory so that you sort of know what you need to do.
