Data Sufficiency

In the graph above, the equation of line m is y = ax + b. What is the value of q?

(1) b=2

(2) a=−1/2

The OA is C.

I don't understand why that is the correct answer? Please, can any expert help me with this DS question? Thanks.

Here's the graph.

AAPL wrote:
In the graph above, the equation of line m is y = ax + b. What is the value of q?

(1) b=2

(2) a=−1/2

The OA is C.

I don't understand why that is the correct answer? Please, can any expert help me with this DS question? Thanks.

Notice that 'q' is the x-intercept - the value of x when y = 0, or when the line crosses the x-axis. If the equation of the line is y = ax + b, then we can find the algebraic expression for the x-intercept by setting y = 0 and solving for x.

0 = ax + b --> -b = ax ---> -b/a = x.

Rephrased Question: What is the value of (-b/a) ?

1) This gives us 'b,' but 'a' could be anything. Put another way, knowing the y-intercept alone can't tell us what the x-intercept is. Not sufficient.

2) This gives us 'a,' but 'b' could be anything. Put another way, knowing the slope alone can't tell us what the x-intercept is. Not sufficient

Together. We want -b/a. We have a value for 'b' and a value for 'a,' so clearly we can determine the value of -b/a. The statements together are sufficient. The answer is C

See here for another official question in which knowing the x-intercept formula is helpful: https://www.beatthegmat.com/in-the-xy-pl ... 92142.html