Write an equation in slope-intercept form of the line that is perpendicular to the one given point.
(4,8); y=-2x-4
the new line is perpendicular to y = -2x + 4
so it must be
y = (1/2)x + b, but (4,8) is to lie on it, thus
8 = (1/2)(4) + b
8 = 2 + b
b = 6
y = (1/2)x + 6
Thanks
To find the equation of a line that is perpendicular to a given line, we need to determine the slope of the given line and then find the negative reciprocal of that slope.
The given line has a slope of -2, so the slope of the line perpendicular to it would be the negative reciprocal of -2, which is 1/2.
To derive the equation of the line using the slope-intercept form (y = mx + b), we also need a point on the new line. The problem provides the point (4,8).
Now that we have the slope and a point, we can substitute these values into the slope-intercept form to find the equation:
y = mx + b
The slope (m) is 1/2, so the equation becomes:
y = (1/2)x + b
To find the value of b, we substitute the coordinates of the given point (4,8) into the equation:
8 = (1/2)(4) + b
We simplify:
8 = 2 + b
Subtracting 2 from both sides:
6 = b
Finally, we substitute the value of b back into the equation:
y = (1/2)x + 6
So, the equation of the line perpendicular to the given line and passing through the point (4,8) is y = (1/2)x + 6.