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SAT Math: Geometry

Coordinate Geometry

In the xy-coordinate plane, line m is parallel to the x axis, and it passes through the point (4, -7).  Which of the following is an equation for line m?

A. x = -4
B. y = 4
C. y = -7
D. y + 7 = x - 4
E.  y – 7 = x + 4

Knowsys Method

Read the problem carefully.  Take careful note that the line in the question is parallel to the x axis.  

Identify the bottom line.  equation for line m = ?

Assess your options.  We must solve this problem by plugging the line into the point-slope formula.  The point slope formula is:

Screen Shot 2014-01-03 at 4.28.28 PM.jpg

Attack the problem.  We need to use the point-slope formula, but to do so, we must determine the slope (m) and the y-intercept (b).  It makes it a little easier to explain this problem if we draw out the line on the coordinate grid, but you do not have to do this step.  

Screen Shot 2014-01-03 at 4.23.46 PM.jpg

As the illustration shows, line m is parallel to the x axis, which makes it is a completely horizontal line.  A horizontal line has a slope of 0.  Think about it: if the y value never changes, then the change in y is zero, and no matter what the change in x, 0 divided by anything is 0.  Since you know that the y value never changes, you also know the y-intercept will be (0,-7).  Plug these values into the point-slope formula.

y = mx + b
y = (0)x -7
y = -7

Loop back.  Verify that you solved for the bottom line.

The correct answer is C.
This is a medium level problem.

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