Find the equation of a line that is perpendicular to the line y = 1/4x + 5 and contains the point (-6, 0)
Y=________ (Type your answer in slope-intercept form.)
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the perpendicular line has slope -4
Now you have a point and a slope, so use the point-slope form of the line. Then rearrange to slope-intercept form.
To find the equation of a line that is perpendicular to the line y = 1/4x + 5, we need to determine the slope of the line we want to find.
The given line has a slope of 1/4. The slope of a line perpendicular to this line will be the negative reciprocal of the given slope.
So, the slope of the line we want to find is -4/1 or -4.
We also have a point that the line needs to pass through, which is (-6, 0).
Now, we can use the point-slope form of a line to find the equation.
The point-slope form is given by: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Plugging in the values, we have:
y - 0 = -4(x - (-6))
Simplifying further:
y = -4(x + 6)
Expanding the equation:
y = -4x - 24
Hence, the equation of the line that is perpendicular to y = 1/4x + 5 and passes through the point (-6, 0) is y = -4x - 24.