In the xy-Plane, a Line has Slope 3 and x-Intercept 3 GMAT Problem Solving

Question: In the xy-plane, a line has slope 3 and x-intercept 3. What is the y-intercept of the line?

1. -9
2. -3
3. 0
4. 3
5. 9

Correct Answer: A
Solution and Explanation:
Approach Solution 1:
x intercept 3 means the line passes through (3, 0). Slope of 3 means y coordinate increases by 3 units for every 1 unit rise in x co-ordinate or y coordinate decreases by 3 units for every 1 unit decrease in x coordinate.
At y intercept, x coordinate is 0. So if we reduce x by 3 (to go from 3 to 0), y will reduce by 9.
So, the line will pass through (0, -9)

Approach Solution 2:
Let the line be represented by a general equation y=mx+b, where m = slope (3) and b=y intercept. We are also given the value of x-intercept 3.
Theory : y intercept represents the point on the line where the x=0, and x intercept represents the point on the line where the y=0.
Putting these values in the equation : 0 = 3*3 + b => b = -9.

Approach Solution 3:
We know equation of a line is
y = mx + C
Now, as given at X =3, y = 0, we can get below,
0 = 3*3 + C => C = -9
Now, the question has asked for y intercept which is nothing but C in the equation y = mx+C.
we can even cross verify by substituting again –
y = 3*0 = (-9) = -9

“In the xy-plane, a line has slope 3 and x-intercept 3.”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide". To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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