Question

Write an equation of the line containing the point (3,1) and perpendicular to the line 2x - 3y = 4.The equation of the line is____(Type an equation. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation. Simplify your answer. Do notfactor.)

Answer 1

Two lines are perpendicular when the multiplication of their slopes is equal to -1.

To find the slope of the line 2x - 3y = 4, we have to isolate y, as follows:

`\begin{gathered} 2x-3y=4 \\ -3y=4-2x \\ y=(4-2x)/(-3) \\ y=(4)/(-3)+(-2x)/(-3) \\ y=-(4)/(3)+(2)/(3)x \end{gathered}`

Its slope is 2/3, then the slope of the perpendicular line is:

`\begin{gathered} m\cdot(2)/(3)=-1 \\ m=-1\cdot(3)/(2) \\ m=-(3)/(2) \end{gathered}`

The slope-intercept form is:

y = mx + b

where m is the slope and b is the y-intercept.

Replacing with m = -3/2 and point (3,1):

1 = -3/2(3) + b

1 = -9/2 + b

1 + 9/2 = b

11/2 = b

The equation of the line is y = -3/2x + 11/2