Use the expressions $f(x)=4x-7$ and $g(x)=-2x+5$. If their $y$-values are the same at the intersection, what equation can you write relating $4x-7$ and $-2x+5$?

After you set $4x-7$ equal to $-2x+5$, combine like terms step by step: move all $x$ terms to one side and constants to the other. Be careful with the signs when you add or subtract terms.

Once you find an $x$-value, plug it into both $f(x)$ and $g(x)$. If the $y$-values match, you have the correct intersection $x$-value.

In Desmos, enter y = 4x - 7 on one line and y = -2x + 5 on another line so you can see both lines on the same coordinate plane.

Click or tap near where the two lines cross; Desmos will mark the intersection point. Read off the $x$-coordinate of that intersection point—this is the $x$-value where the graphs intersect.

When two graphs intersect, they share a point with the same $x$-value and the same $y$-value. That means at the intersection point, $f(x)=g(x)$.

So set the two expressions equal:

To solve for $x$, first move the $-2x$ term to the left by adding $2x$ to both sides:

which simplifies to

Now move the constant term $-7$ to the right by adding $7$ to both sides:

so

Now divide both sides of $6x = 12$ by $6$:

So, the graphs of $f$ and $g$ intersect at $x = 2$. This is the value you should enter.