Question

What is the equation of a line, in point- slope form, that passes through (5, -3) and has a slope of 2/3?

a. y−3=23(x+5)

b. y+3=23(x−5)

c. y+5=23(x−3)

d. y−5=23(x+3)

Answer 1

Option B

The equation of a line, in point- slope form, that passes through (5, -3) and has a slope of 2/3

`y + 3 = (2)/(3)(x -5)`

Solution:

The equation of line in point slope form is given as:

`y - y_1 = m(x-x_1)`

Where, "m" is the slope of line

Given that,

slope = 2/3

`m = (2)/(3)`

The line passes through (5, -3)

Substitute m = 2/3 and
`(x_1, y_1)` = (5, -3) in point slope form

`y - (-3) = (2)/(3)(x -5)\\\\y + 3 = (2)/(3)(x -5)`

Thus equation of line in point slope form is found