What is the slope of any line perpendicular to the line 4x-2y=10 ?
2 y = 4 x = 10
y = 2 x - 5
so m = slope = 2
To find the slope of any line perpendicular to another line, we first need to determine the slope of the given line.
The given line is in the form of a linear equation in the standard form: Ax + By = C. Rearranging the given equation to slope-intercept form, y = mx + b, will help us determine the slope.
Let's rearrange the equation 4x - 2y = 10 to solve for y:
4x - 2y = 10
-2y = -4x + 10
Dividing both sides of the equation by -2:
y = 2x - 5
Now we can see that the slope of the given line is 2.
To find the slope of any line perpendicular to this line, we need to use the property that perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of any line perpendicular to it will be -1/m.
Therefore, the slope of any line perpendicular to 4x - 2y = 10 is -1/2.