(SHOW WORK) Write the slope-intercept form of the equation: passes through (-2, 3) and is perpendicular to y = 1/4x - 4

Step-by-step explanation:

We want to find the slope-intercept form of the equation that passes through the point (-2, 3) and is perpendicular to the line:

Note that this line has a slope of 1/4.

Recall that the slopes of perpendicular lines are negative reciprocals of each other.

Since the slope of our old line is 1/4, the slope of its perpendicular line must be -4.

We are also given that it passes through the point (-2, 3). So, we can consider using point-slope form:

Let (-2, 3) be (x₁, y₁) and substitute -4 for the slope m. Hence:

Convert into slope-intercept form. Simplify:

In conclusion, the perpendicular line that passes through the point (-2, 3) is given by: