Question

Given the points (5, 2) and (7, 10) find the slope of the line going through the two points . Now write the point-slope form of the equation of the line going through the two points Question 2 What is the equation of a line in point-slope form that passes through (4, -2) and (0, -5). y - 4 = -3/4(x - (-2)) y - 4 = -3/4(x - (-2)) y - 0 = 4/3(x - (-5)) y - 0 = 4/3(x - (-5)) y - (-2) = 3/4(x - 4) y - (-2) = 3/4(x - 4) y - (-5)) = 3/4(x - 0) y - (-5)) = 3/4(x - 0)

Answer 1

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.