Find the equation of a line that is perpendicular to y=2x+7, and passes through the point (-4, 7)
I got the answer y=-1/2x+5, is that the correct equation??
got the right slope
point-slope ... y - 7 = -1/2 (x + 4)
equation looks good
so scott my equation is right
easiest way:
Since the slopes must be negative reciprocals of each other, the new equation must look like this
y = (-1/2)x + b
plug in your point (-4,7)
7 = (-1/2)(-4) + b
5 = b
y = (-1/2)x + 5
To find the equation of a line perpendicular to another line, you need to determine the slope of the given line and then find the negative reciprocal of that slope.
The slope-intercept form of a line is given by y = mx + b, where m represents the slope of the line. In the given line equation y = 2x + 7, the slope is 2, since the coefficient of x is 2.
Now, to find the slope of the line perpendicular to this, you take the negative reciprocal of the slope. The negative reciprocal of 2 is -1/2.
So, the slope of the line perpendicular to y = 2x + 7 is -1/2.
Next, we have the point (-4, 7) through which the perpendicular line must pass.
Using the point-slope form of a line, which is y - y₁ = m(x - x₁), where (x₁, y₁) represents the given point and m is the slope, we can substitute the values to find the equation of the line.
Substituting x₁ = -4, y₁ = 7, and m = -1/2 into the point-slope form, we get:
y - 7 = -1/2(x - (-4))
Simplifying the equation gives:
y - 7 = -1/2(x + 4)
Expanding the equation further:
y - 7 = (-1/2)x - 2
And finally, rearranging the equation to the slope-intercept form gives us:
y = (-1/2)x + 5
Therefore, the correct equation of the line perpendicular to y = 2x + 7 and passing through the point (-4, 7) is y = (-1/2)x + 5.
So, your answer is correct!