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
\[
x=
\]
Final Answer: \(x = \boxed{2}\)
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: \(x = \boxed{2}\)