Questions: What is the equation of the line that is perpendicular to the line y=3x+7 that goes through the point (3,4)?

Transcript text: What is the equation of the line that is perpendicular to the line $y=3 x+7$ that goes through the point $(3,4)$ ?

Solution

Solution Steps

Step 1: Calculate the slope of the perpendicular line

To find a line perpendicular to the given line $y = 3x + 7$, we calculate the negative reciprocal of the given slope $m$. The slope of the perpendicular line, $m'$, is $-\frac1{3}$ which rounds to -0.33 when rounded to 2 decimal places.

Step 2: Use the point-slope form to find the equation of the perpendicular line

Using the point $(3, 4)$ and the slope $m' = -0.33$, we apply the point-slope form $y - y_1 = m'(x - x_1)$. Simplifying this to the slope-intercept form gives us the equation of the line: $y = -0.33x + 5$.