Question

Find the equation of a line perpendicular to 5x−3y=−2 that contains the point (-4,5). Write the equation in slope-intercept form.

a) y=(3/5)x+13/5
b) y=(5/3)x−23/3
c) y=(3/5)x−23/5
d) y=(5/3)x+13/3

Answer 1

To find the equation of a line perpendicular to 5x - 3y = -2 that contains the point (-4, 5), we need to find the negative reciprocal of the slope of the given line. The equation of the perpendicular line is y = (-3/5)x + 13/5.

Step-by-step explanation:

To find the equation of a line perpendicular to a given line, we need to find the negative reciprocal of the slope of the given line. The given line has the equation 5x - 3y = -2. To find the slope, we rearrange the equation in slope-intercept form: y = (5/3)x + 2/3. The slope of the given line is 5/3, so the slope of the perpendicular line is -3/5.

Using the point-slope form of a line, we can write the equation of the perpendicular line using the point (-4, 5) and the slope -3/5: y - 5 = -3/5(x - (-4)). Simplifying this equation, we get y = (-3/5)x + 13/5.

Therefore, the equation of the line perpendicular to 5x - 3y = -2 that contains the point (-4, 5) is y = (-3/5)x + 13/5.