49.9k views
5 votes
Write the equation of the line perpendicular to y=4/5x+2/5 that passes through the point (-7,3).

User Daniil
by
8.2k points

1 Answer

5 votes

Final answer:

The equation of the line perpendicular to y=4/5x+2/5 and passing through the point (-7,3) is y = (-5/4)x - (23/4).

Step-by-step explanation:

To find the equation of the line perpendicular to y=4/5x+2/5 that passes through the point (-7,3), we first determine the slope of the given line. Perpendicular lines have slopes that are negative reciprocals of each other. Since the slope of the given line is 4/5, the perpendicular slope would be -5/4.

Now, we use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Substituting the point (-7, 3) and the perpendicular slope -5/4, we get:

y - 3 = (-5/4)(x + 7)

To convert to slope-intercept form (y = mx + b), we distribute and simplify:

y = (-5/4)x - (35/4) + 3
y = (-5/4)x - (35/4) + (12/4)
y = (-5/4)x - (23/4)

Therefore, the equation of the line perpendicular to y=4/5x+2/5 and passing through the point (-7,3) is y = (-5/4)x - (23/4).

User PT Vyas
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories