Write an equation for the line that passes through (0,7) and is perpendicular to the line whose equation is y=1/2x-1.
y-y1=m(x-x1)
y-7=2/1(x-0)
y-7=2x-0
y=2x+7(answer)
The slope of the line you want is -2.
(y-7) = -2(x-0)
y = -2x + 7
Where did you get negative 2??
The product of the slopes of two perpendicular lines has to be -1. That should be in your textbook or class notes somewhere.
(1/2) * -2 = -1
Well, well, look who's perpendicular! It seems we have a line that's going against the flow and crossing paths at a right angle with the line y = 1/2x - 1. The equation for this rebellious line would be y = 2x + 7. Keep in mind, this line is not afraid to take a different direction, so don't go underestimating its uniqueness!
To find the equation for a line perpendicular to another line, we need to determine the slope of the given line and then take the negative reciprocal of that slope.
The given line has the equation y = (1/2)x - 1. To determine the slope, we can see that the coefficient of x is 1/2. The slope of this line is 1/2.
To find the slope of the line perpendicular to this, we take the negative reciprocal of 1/2. The negative reciprocal of 1/2 is -2. Therefore, the slope of the perpendicular line is -2.
We also know that this line passes through the point (0,7). We can substitute the coordinates of this point into the equation y = mx + b, where m is the slope, to solve for b (the y-intercept).
Using the point (0,7), we substitute x=0 and y=7 into the equation:
7 = -2(0) + b
7 = b
So the y-intercept, b, is 7.
Now we have the slope (-2) and the y-intercept (7), we can form the equation of the line using the slope-intercept form:
y = mx + b
y = -2x + 7
Therefore, the equation of the line that passes through (0,7) and is perpendicular to the line y = (1/2)x - 1 is y = -2x + 7.