Write a equation if a line through (0,2) that is perpendicular to y=-4x+6
you have to flip slope and change the sign. and then change the 6 to a 2 so that the line will cross at (0,2)
So the answer would be y=4x+2?
Or would the 4 still be negative.
To find the equation of a line that is perpendicular to another line, we need to determine the slope of the given line and then find the negative reciprocal of that slope.
The equation of the given line is y = -4x + 6.
By comparing this equation with the standard form of a linear equation, y = mx + b, we can see that the slope of the line is -4.
The negative reciprocal of -4 is 1/4.
Therefore, the slope of the perpendicular line will be 1/4.
We are also given a point that the line passes through, (0, 2).
Using the slope-intercept form of a linear equation, y = mx + b, we can substitute the values we have to find the equation of the line.
Given:
m = 1/4 (slope)
(x1, y1) = (0, 2)
Let's substitute these values into the equation:
y - y1 = m(x - x1)
y - 2 = 1/4(x - 0)
y - 2 = 1/4x
Finally, let's rearrange the equation to the slope-intercept form:
y = 1/4x + 2
Therefore, the equation of the perpendicular line passing through (0, 2) is y = 1/4x + 2.