Write an equation of a line perpendicular to y=1/2x-5 in slope-intercept form that passes through the point (2, -7).
Why did the perpendicular line go to the therapist?
Because it needed to find its slope-intercept!
But don't worry, I'm here to help!
The given equation is y = 1/2x - 5, and we know that a line perpendicular to it will have a slope that is the negative reciprocal of 1/2.
Since 1/2 in decimal form is 0.5, the negative reciprocal would be -2.
So, we have our slope for the perpendicular line. Now let's use the point-slope form of a linear equation to find the equation.
The point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line.
Using the point (2, -7), the equation becomes y - (-7) = -2(x - 2).
Simplifying this equation, we have y + 7 = -2x + 4.
Now, let's rearrange it to the slope-intercept form, which is y = mx + b.
Subtracting 7 from both sides, we get y = -2x + 4 - 7.
Simplifying further, the equation of the line perpendicular to y = 1/2x - 5 and passing through (2, -7) is y = -2x - 3.
Hope that brings a smile to your face!
To find the equation of a line perpendicular to a given line, we need to determine the negative reciprocal of the slope of the given line.
The given line has a slope of 1/2. To find the negative reciprocal, we flip the fraction and change its sign. So the negative reciprocal of 1/2 is -2.
Now that we know the slope of the new line, and we have a point it passes through (2, -7), we can use the point-slope form to find the equation.
The point-slope form of a linear equation is: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
Plugging in the values we have:
y - (-7) = -2(x - 2)
Simplifying:
y + 7 = -2(x - 2)
Expanding the brackets:
y + 7 = -2x + 4
Rearranging the equation to slope-intercept form:
y = -2x + 4 - 7
Simplifying further:
y = -2x - 3
Therefore, the equation of the line perpendicular to y = 1/2x - 5 that passes through the point (2, -7) is y = -2x - 3.
The key to perpendicular lines is that the slopes will multiply together to get negative one. Since your original slope is 0.5, your new slope will be -2. Passing through your stated points, the point-slope equation of the line will be:
y-(y1)=m(x-(x1))
plug in your slope & points..
y+7=2(x-2) , simplified, this gives you
y=2x-11
Hope this helps!
Wow thanks! It is correct! :D
slope of new line must be -2
so y =-2x + b
plug in the given point (2,-7)
-7 = -2(2) + b
-3 = b
y = -2x - 3
I forgot the - in the above answer that I gave. It should really be
y+7=-2(x-2)
y=-2x-3