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

Sagot :

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:

[tex]\begin{gathered} m\cdot3=-1 \\ m=-\frac{1}{3} \end{gathered}[/tex]

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

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