What is an equation of a line, in point-slope form, that passes through (1, −7) and has a slope of −23 ?

y+7=23(x+1)?
y−7=−23(x+1)?
y−7=23(x−1)?
y+7=−23(x−1)

in slope form

point slope form: y-y1=m(x-x1)

coordinate (1,-7):

point y1--7

point x1=1

slope (m)=-23

input into equation:

y-(-7)=-23(x-1)

convert to slope intercept form:

-*-=+ so 7 becomes +7

y+7

distribute -23 in -23(x-1) using the rule: a(b+c)=ab+ac

-23x+23

refine

y+7=-23x+23

perform some inverse operations:

y+7=-23x+23

y+7=-23x+23-7

y=-23x+16

therefore, D. y+7=−23(x−1) equals y=-23x+16 in slope-intercept form