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
The equation of a line that is perpendicular to y = 5x - 7 would have a slope that is the negative reciprocal of 5. The slope of y = 5x - 7 is 5, so the slope of the perpendicular line would be -1/5.
Using the point-slope form of a linear equation, y - y1 = m(x - x1), with the point (-10, 3) and the slope -1/5, we can plug in the values to find the equation:
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.
So the correct response is: y = -1/5x + 1.
To find the equation of a line that is perpendicular to y = 5x - 7 and passes through (-10, 3), we need to determine the slope of the given line and then find the negative reciprocal of that slope.
The given line has a slope of 5 (the coefficient of x). The negative reciprocal of 5 is -1/5.
Now we can use the point-slope form of a linear equation to write the equation of the perpendicular line.
y - y1 = m(x - x1)
Plugging in the values: (x1, y1) = (-10, 3) and m = -1/5
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.
To find the equation of a line that is perpendicular to y = 5x - 7 and passes through (-10, 3), we need to determine the slope of the given line and use it to find the slope of the perpendicular line.
The given line is in slope-intercept form, y = mx + b, where m is the slope. In this case, the slope is 5.
For two lines to be perpendicular, the product of their slopes must be -1. So, the slope of the perpendicular line will be the negative reciprocal of the given line's slope.
The negative reciprocal of 5 is -1/5.
Now that we have the slope of the perpendicular line and a point that lies on it (-10, 3), we can use the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) are the coordinates of the given point, and m is the slope of the line.
Plugging in the values, we get:
y - 3 = (-1/5)(x + 10)
Simplifying:
y - 3 = (-1/5)x - 2
Adding 3 to both sides:
y = (-1/5)x + 1
So, the equation of the line that passes through (-10, 3) and is perpendicular to y = 5x - 7 is y = (-1/5)x + 1.