Question

A line passes through the point (–6, –3) and has a slope of 2/3 . Which point is on the same line?

Answer 1

The point (0, 1) represents the y-intercept.

Hence, the y-intercept (0, 1) is on the same line.

Explanation:

We know that the slope-intercept form of the line equation

y = mx+b

where

• m is the slope

• b is the y-intercept

Given

• The point (-6, -3)

• The slope m = 2/3

Using the point-slope form

`y-y_1=m\left(x-x_1\right)`

where

• m is the slope of the line

• (x₁, y₁) is the point

In our case:

• m = 2/3

• (x₁, y₁) = (-6, -3)

substituting the values m = 2/3 and the point (-6, -3) in the point-slope form

`y-y_1=m\left(x-x_1\right)`

`y-\left(-3\right)=(2)/(3)\left(x-\left(-6\right)\right)`

`y+3=(2)/(3)\left(x+6\right)`

Subtract 3 from both sides

`y+3-3=(2)/(3)\left(x+6\right)-3`

`y=(2)/(3)x+4-3`

`y=(2)/(3)x+1`

comparing with the slope-intercept form y=mx+b

Here the slope = m = 2/3

Y-intercept b = 1

We know that the value of y-intercept can be determined by setting x = 0, and determining the corresponding value of y.

Given the line

`y=(2)/(3)x+1`

at x = 0, y = 1

Thus, the point (0, 1) represents the y-intercept.

Hence, the y-intercept (0, 1) is on the same line.