Question

through the point (4,10) and is perpendicul to the line y = -4x - 6.

Explanation:

Step1: Find slope of perpendicular line

The slope of $y=-4x-6$ is $m_1=-4$. The slope of a perpendicular line is the negative reciprocal: $m_2=\frac{1}{4}$

Step2: Use point-slope form

Point-slope formula: $y-y_1=m(x-x_1)$. Substitute $(x_1,y_1)=(4,10)$ and $m=\frac{1}{4}$:
$y-10=\frac{1}{4}(x-4)$

Step3: Simplify to slope-intercept form

Expand and isolate $y$:
$y-10=\frac{1}{4}x - 1$
$y=\frac{1}{4}x -1 +10$
$y=\frac{1}{4}x +9$

Answer:

$y=\frac{1}{4}x + 9$