Question
Which equation is the equation of a line that passes through (–10, 3) and is perpendicular to y = 5x – 7? (1 point) Responses y = 5x + 53 y = 5 x + 53 y = –x – 7 y = – Image with alt text: one-fifth x – 7 y = –x + 1 y = – Image with alt text: one-fifth x + 1 y = x + 5
Answers
GPT 3.5
To find the equation of a line that is perpendicular to y = 5x - 7, we need to find its slope and then use the point-slope form to write the equation.
The given equation is y = 5x - 7.
The slope of this line is 5.
The slope of a line perpendicular to this line will be the negative reciprocal of 5, which is -1/5.
Using the point-slope form, the equation will be y - y1 = m(x - x1), where (x1, y1) is the given point (-10, 3).
Substituting the values, we have:
y - 3 = -1/5(x - (-10))
y - 3 = -1/5(x + 10)
y - 3 = -1/5x - 2
y = -1/5x + 1
Therefore, the equation of the line that passes through (-10, 3) and is perpendicular to y = 5x - 7 is y = -1/5x + 1.
The given equation is y = 5x - 7.
The slope of this line is 5.
The slope of a line perpendicular to this line will be the negative reciprocal of 5, which is -1/5.
Using the point-slope form, the equation will be y - y1 = m(x - x1), where (x1, y1) is the given point (-10, 3).
Substituting the values, we have:
y - 3 = -1/5(x - (-10))
y - 3 = -1/5(x + 10)
y - 3 = -1/5x - 2
y = -1/5x + 1
Therefore, the equation of the line that passes through (-10, 3) and is perpendicular to y = 5x - 7 is y = -1/5x + 1.