How do you graph #y=1/4x -5#?

1 Answer
Jun 18, 2017

Answer:

See below

Explanation:

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.