Consider the functions 𝑔 and ℎ given by 𝑔𝑥=4𝑥 and ℎ𝑥=16𝑥+2. In the 𝑥𝑦-plane, what is the 𝑥-coordinate of the point of intersection of the graphs of 𝑔 and ℎ ?

Question

$g(x) = 4x$
and
$h(x) = 16x + 2$ .
In the $xy$ -plane, what is the $x$ -coordinate of the point of intersection of the graphs of $g$ and $h$ ?

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To find the x-coordinate of the point of intersection of the graphs of g and h, we need to set the two functions equal to each other and solve for x.

So, we have:

4x = 16x + 2

To solve for x, we first subtract 16x from both sides to get:

-12x = 2

Then, we divide both sides by -12 to solve for x:

x = 2 / -12

Simplifying the fraction, we get:

x = -1/6

So, the x-coordinate of the point of intersection of the graphs of g and h is -1/6.

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