Problem 52

Question

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through $(-4,2)$ and perpendicular to the line whose equation is $y=\frac{1}{3} x+7$

Step-by-Step Solution

Verified

Answer

The equation of the line is $y - 2 = -3(x + 4)$ in point-slope form and $y = -3x - 10$ in slope-intercept form.

1Step 1: Identify the slope of the given line

The slope of the given line $y = \frac{1}{3}x + 7$ is $\frac{1}{3}$, identified by extracting the coefficient of $x$.

2Step 2: Find the slope of the perpendicular line

The slope of the line perpendicular to the given line is the negative reciprocal of the slope of given line. Hence, the slope of the required line is $-1/\frac{1}{3} = -3$.

3Step 3: Write the equation of the line in point-slope form

Employing the coordinates of the given point $(-4,2)$ and the perpendicular slope $-3$, the point-slope form of the line is : $y - 2 = -3(x + 4)$.

4Step 4: Convert equation to slope-intercept form

To convert to slope-intercept form, which is $y = mx + c$, simplify the point-slope equation: $y = -3x - 10$.

Problem 51

Problem 52