Write an equation in slope intercept form of the line that passes through the given point and is perpendicular to the graph of the given equation.

(1,-6). X-2y=4

easiest way:

since the new line is to be perpendicular to
x - 2y = 4 ,

the new line must be 2x + y = c
plug in (-1,6) to find c

all done

To find the equation of a line that is perpendicular to the given line, we need to first determine the slope of the given line. The slope-intercept form of a line is given by the equation y = mx + b, where m represents the slope of the line.

Let's rewrite the equation in slope-intercept form:

x - 2y = 4
-2y = -x + 4
y = (1/2)x - 2

From the equation y = (1/2)x - 2, we can see that the slope of the given line is 1/2.

To find the slope of a line that is perpendicular to this line, we need to take the negative reciprocal of the slope. The negative reciprocal of 1/2 is -2/1, which can be simplified to -2.

Now that we have the slope of the perpendicular line, we can use the given point (1, -6) to find the equation.

Using the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is the given point, and m is the slope:

y - (-6) = -2(x - 1)
y + 6 = -2x + 2
y = -2x - 4

Therefore, the equation in slope-intercept form of the line that passes through the point (1, -6) and is perpendicular to the graph of x - 2y = 4 is y = -2x - 4.