Question

Which is the graph of the line with equation y−4=2(x+1)?

Number graph ranging from negative three to three on the x axis and negative seven to one on the y axis. A line is drawn on the graph that passes through the points (zero, negative six) and (three, zero).


Number graph ranging from negative four to three on the x axis and negative five to two on the y axis. A line is drawn on the graph that passes through the points (zero, negative four) and (one, zero).


Number graph ranging from negative three to three on the x axis and negative two to four on the y axis. A line is drawn on the graph that passes through the points (negative one, zero) and (zero, four).


Number graph ranging from negative three to three on the x axis and negative one to six on the y axis. A line is drawn on the graph that passes through the points (negative three, zero) and (zero, six).

Answer 1

Answer: D. "Number graph ranging from negative three to three on the x axis and negative two to four on the y axis. A line is drawn on the graph that passes through the points (negative one, zero) and (zero, four)."

Explanation:

We know that our graph passes through two given sets of points, therefore we can plug in those points to find the correct answer.

Let's test it with choice A. It gives us the points (0,-6) and (3,0). We can plug these into the equation to see if it is true. y-4 = 2(x+1) becomes
-6-4 = 2(3+1), or -10 = 8 which is not true, so we can eliminate it.

Choice B gives us (0,-4) and (1,0) -4-4 = 2(0+1) or -8 = 2, this one is wrong.

Choice C gives us (-1,0), so 0-4 = 2(-1+1) or -4 = 0, this one is also wrong.

Choice D gives us (-3,0) so 0-4 = 2(-3+1) or -4 = -4. This is the only option which has a correct solution, and therefore it is your answer.

Answer 2

Number graph ranging from negative three to three on the x axis and negative one to six on the y axis. A line is drawn on the graph that passes through the points (negative three, zero) and (zero, six).

Explanation:

Simplified y-4 = 2(x + 1) ⇒ y = 2x + 6

Graphed function on desmos graphing calculator

Matched the through points of option #4, (-3, 0) and (0 ,6) to the graph.