bettatantalo wrote:

At which point do the following lines intersect?

f(x)=−4x+3

g(x)=5x+39

a) (-4,39)

b) (-4,19)

c) (0,0)

d) (4,-39)

e) (4,19)

source gmat tutor

\(f(x)=y\) and \(g(x)=y\)

Just rewrite f(x) and g(x) as \(y\). Doing so yields two linear equations in slope-intercept form*: \(y=mx+b\)

So \(f(x)=−4x+3\) becomes

\(y=-4x+3\)

AND

\(g(x)=5x+39\) becomes

\(y=5x+39\)

At the point of intersection, lines, expressed by their equations, have the same (x,y) coordinates.

We use \(y=y\) from equations above to find the x-coordinate.

Set the linear equations equal:

\(-4x +3 = 5x+39\)

\(-9x=36\)

\(x =\frac{36}{-9}=-4\)

The lines intersect at x-coordinate (-4). Plug that (-4) back into either equation to find the y-coordinate

\(y= -4x +3\)

\(y =(-4)(-4)+3\)

\(y=(16+3)=19\)

The point of intersection (x,y) is (-4,19)

Answer B

*

\(y = f(x) = mx + b\)

\(y=mx+b\)

is slope-intercept form

See HERE for a good explanation of slope intercept form.

Linear functions have one dependent variable, y, and one independent variable, x. Similarly, the slope-intercept form of an equation also has dependent variable \(y\) and independent variable \(x\)
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