Question

The line contains the point (-3,5) and is perpendicular to the line y=3x-4

Answer 1

two lines are perpendicular when the multiplication of their slopes is equal to -1. The slope of y = 3x - 4 is 3. Then the slope of a perpendicular line ​is:

`\begin{gathered} m\cdot3=-1 \\ m=-(1)/(3) \end{gathered}`

Slope-intercept form:

y = mx + b

where m is the slope and b is the y-intercept. Replacing with point (-3, 5) and m = -1/3, we get:

5 = -1/3(-3) + b

5 = 1+ b

5 - 1 = b

4 = b

Then, the equation is:

y = -1/3x + 4