Passes through (1, 1) and perpendicular to y= -1/2x
+4.
To find an equation that passes through the point (1, 1) and is perpendicular to the line y = (-1/2)x + 4, we need to follow these steps:
1. Determine the slope of the given line. The slope of a line in the form y = mx + b is given by m. In this case, the slope is -1/2.
2. Since the line we want to find is perpendicular, the slope of the new line will be the negative reciprocal of the given line's slope. To find the negative reciprocal, we take the reciprocal (flipping the fraction) and change the sign. So, the slope of the new line will be 2.
3. Now we have the slope (m = 2) and a point (1, 1) that the line passes through. We can use the point-slope form of a linear equation to find the equation.
The point-slope form of a linear equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Using the point (1, 1) and the slope m = 2, we have:
y - 1 = 2(x - 1)
4. Simplify the equation:
y - 1 = 2x - 2
5. Move the constant term to the opposite side of the equation:
y = 2x - 2 + 1
y = 2x - 1
So, the equation of the line that passes through the point (1, 1) and is perpendicular to y = (-1/2)x + 4 is y = 2x - 1.