Find the value of $x$ so that the line through the pair of points has the given slope. Points $(x, 4)$ and $(4,12)$ Slope 4 \[ x= \]

Step 1 ：The slope of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula \(\frac{y_2 - y_1}{x_2 - x_1}\).

Step 2 ：In this case, we know the slope is 4, and we have the points \((x, 4)\) and \((4,12)\).

Step 3 ：We can substitute these values into the slope formula and solve for \(x\).

Step 4 ：Setting up the equation, we get \(4 = \frac{12 - 4}{4 - x}\) which simplifies to \(4 = \frac{8}{4 - x}\).

Step 5 ：Solving this equation gives us \(x = 2\).

Step 6 ：This means that the value of \(x\) that makes the line through the points \((x, 4)\) and \((4,12)\) have a slope of 4 is 2.

Step 7 ：Final Answer: \(x = \boxed{2}\)