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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