Question

What is the equation of the line shown?

Answer 1

y =
`(4)/(3)` x +
`(5)/(3)`

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (- 2, - 1) and (x₂, y₂ ) = (1, 3) ← 2 point on the line

m =
`(3+1)/(1+2)` =
`(4)/(3)` , then

y =
`(4)/(3)` x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (1, 3 ), then

3 =
`(4)/(3)` + c ⇒ c = 3 -
`(4)/(3)` =
`(5)/(3)`

y =
`(4)/(3)` x +
`(5)/(3)` ← equation of line

Answer 2

Explanation:

Hey there!

According to the figure, we find two points on graph. I.e (1,3) and (-2,-1) points respectively.

Now, Use double point formula for finding the eqaution.

`(y - y1) = (y2 - y1)/(x2 - x1) (x - x1)`

Keep all values.

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

~ Simplify it.

`(y - 3) = (4)/(3) (x - 1)`

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

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

`y = (4)/(3) x + (5)/(3)`

Therefore, the equation of the line is y= 4/3x + 5/3.

Hope it helps...