Rank: Easy
Topic: Algebra, Equation of a line

Below is a question from a recent SAT exam. It is a non-calculator question that would typically take a student 1-2 minutes to complete.

Which of the following is an equation of line ℓ in the
xy-plane above?

(A) x – y = –4
(B) x – y = 4
(C) x+ y = –4
(D) x+ y = 4

To begin, we must recall that the equation on a straight line comes in the form

Where m is the slope and c is the y-intercept.
We will start by finding the y-intercept. This is the point where the line crosses the y-axis.

We can clearly see in this diagram that the line meet the y-axis at -4. So we can replace c in our equation.

Now, we need to find the slope of the line. To find this we use the formula:

So, we need to find to point on our line, any two will do but, I will pick the two points where it meets an axis.
(0,-4) and (-4,0)
So our two x-coordinates are 0 and -4 whilst our two y-coordinates are -4 and 0.
We can put these into the formula:

Therefore,
m=-1
We put this now into our equation for our line.
y=-x-4
We then can move x to the LHS of the equation.
x+y=-4
And we can see that the answer is C.