Step-by-step explanation:
the slope of a line is specified as the ratio y/x. that indicates how many units y changes, when x changes a certain amount of units.
so, going e.g. from (5, 2) to (7, 10), x changes from 5 to 7 = +2 units. and y changes from 2 to 10 = +8 units.
so, the slope y/x = m = 8/2 = 4
the point-slope form is
y - y1 = m(x - x1)
m = slope
(x1, y1) = coordinates of one point on the line. let's pick the first point (5, 2).
y - 2 = 4(x - 5)
or then fully simplified (leading to the slope- intercept form) :
y - 2 = 4x - 20
y = 4x - 18
for question 2 we do the same thing for (4, -2) and (0, -5).
x changes from 4 to 0, so, -4 units.
y changes from -2 to -5, so, -3 units.
slope = y/x = m = -3/-4 = 3/4
since there is a 0 included, let's use (0, -5) as point for the point-slope form
y - -5 = 3/4(x - 0)
or
y + 5 = 3/4 x
so, the last option is correct.
