GMAT question - In the coordinate system above, which of the fol... - Review
Type: Problem Solving
Difficulty: 
In the coordinate system above, which of the following is the equation of line a?
Explanation
You can see from the diagram where the line crosses the y axis at the point (0, 1) and that the line crosses the x axis at the point (-3, 0). See coordinate geometry for more information.
This means that we know that when x = 0 then y = 1 and that when x = -3 then y = 0.
The easiest way to identify the correct equation from this is to substitute the values into the left hand side of each of the equations in answers A to E and eliminate those which are not equal to the right hand side.
A) 3x - y = 3
Substitute and
into
.
So we can eliminate A.
B) 3x + y = 3
Substitute and
into
.
Eliminating B.
C) x + 3y = 3
Substitute and
into
.
So it could still be C
Substitute the other point we know into the left hand side of the equation i.e. and
into
.
So we can eliminate C.
D) 3y - x = -3
Substitute and
into
.
And D can be eliminated
E) 3y - x = 3
Substitute and
into
.
So it could still be E.
Substitute the other point we know into the left hand side of the equation i.e. and
into
.
Which means that E fits both points on the line and is therefore the correct answer.
An easier way would be to calculate the slope of the line, i.e. the value of m. Not sure if we are supposed to use it for GMATS or not but its easier.
Slope of a line y = mx + c is such that m = (y2 - y1)/(x2-x1) where (x1, y1) and (x2, y2) are any 2 points on the line.
In this case we have the 2 points co-ordinates as (0,1) and (-3,0). Plug the values in the slope formula and we get m = (0-1)/(-3-0) = 1/3
c the y-intercept where the line touches the y-axis from graph we can see is (1,0). c is basically the value of x which is 1.
y=mx + c
y=1/3x + 1
3y - x = 3