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

Question

(-2, 3), y = x - 4

Answer 1

Slope intercept form is y = mx + b where m = gradient and b = y intercept.

equation (1) is y = x - 4 is already in this form (if not, rearrange first), m=1 and b = -4

perpendicular lines m1 x m2 = -1 (i.e. each slope is negative inverse of the other)

1 x m2 = -1 => m2 = -1

equation of perpendicular line is y = -x + c (c can be any number, so infinite perpendicular lines)

substitute point values (-2, 3) to find c (the specific value for one particular perpendicular line):

3 = -(-2) + c => 3 - 2 = c => c = 1

hence required equation is y = -x + 1

For these types of questions I highly recommend Desmos graphing to check your work.

Answer 2

slope intercept form is y= mx + b. Need to determine m (slope) and b (y-intercept)

slope of line y=x-4 is 1, so slope of line perpendicular has slope that is negative reciprocal = -1.

so far we have y = -x + b

to find b we substitute given point line passes through (-2,3) for x,y and solve for b:

3 = --2 + b

b = 5

so final equation is y = -x + 5