Question

given the equations of line 1 and line 2 below, which value of $m$ makes the two lines perpendicular? enter the value of $m$ in the box.
line 1: $y = -\frac{1}{4}x + 5$
line 2: $y = mx - 7$
$m = \square$

Explanation:

Step1: Identify slope of Line 1

The slope of Line 1 ($y = -\frac{1}{4}x + 5$) is $m_1 = -\frac{1}{4}$.

Step2: Use perpendicular slope rule

For two lines to be perpendicular, the product of their slopes is $-1$: $m_1 \times m_2 = -1$.
Substitute $m_1 = -\frac{1}{4}$:
$$-\frac{1}{4} \times m = -1$$

Step3: Solve for $m$

Multiply both sides by $-4$:
$$m = (-1) \times (-4) = 4$$

Answer:

$4$