which equation is the equation of a line that passes through (-10 3) and is perpendicular to y=5x-7
y=5x+53
y=-1/5x-7
y=-1/5x+1
y=1/5x+5
pls help? thanks
slope of given line is 5
so the slope of the perpendicular line has to be -1/5
so it could only be B) or C)
but (-10,3) satisfies only equation C)
so C
Yes, thanks Reiny:)
To find the equation of a line that is perpendicular to a given line, we need to find the negative reciprocal of the slope of the given line.
The given line is y = 5x - 7. The slope of this line is 5, so the negative reciprocal of 5 is -1/5.
Now, let's find the equation of the line passing through the point (-10, 3) with a slope of -1/5.
Using the point-slope form of a linear equation, the equation of the line is:
y - y1 = m(x - x1)
where (x1, y1) is the given point.
Substituting (-10, 3) and -1/5 into the equation:
y - 3 = -1/5(x - (-10))
Simplifying:
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. Option C.
To find the equation of a line that is perpendicular to another line, you need to determine the negative reciprocal of the slope of the given line.
The given line equation is y = 5x - 7. Here, the slope of the line is 5 because it is in the form y = mx + b, where m represents the slope.
The negative reciprocal of the slope 5 is -1/5. This means that the perpendicular line will have a slope of -1/5.
Now let's use the coordinates (-10, 3) on the perpendicular line to find the equation.
The general equation for a line is y = mx + b, where m is the slope and b is the y-intercept.
Substituting the slope -1/5 and the point (-10, 3), we have:
3 = (-1/5)(-10) + b
Simplifying the equation:
3 = 2 + b
Subtracting 2 from both sides:
1 = b
So the equation of the perpendicular line is:
y = -1/5x + 1
Therefore, the correct equation for the line that passes through (-10, 3) and is perpendicular to y = 5x - 7 is y = -1/5x + 1.