Question

(3,4) and (12,19) find the equation of the line that passes through it

Answer 1

The equation of the line will be:

`y=(5)/(3)x-1`

Explanation:

Given the points

• (3, 4)

• (12, 9)

Finding the slope between (3, 4) and (12, 9)

`\left(x_1,\:y_1\right)=\left(3,\:4\right),\:\left(x_2,\:y_2\right)=\left(12,\:19\right)`

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`m=(19-4)/(12-3)`

`m=(5)/(3)`

The equation of the line can be obtained using the point-slope form of the equation of the line

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

substituting the values m = 5/9 and the point (3, 4)

`y-4=(5)/(3)\left(x-3\right)`

`y-4+4=(5)/(3)\left(x-3\right)+4`

`y=(5)/(3)x-1`

Therefore, the equation of the line will be:

`y=(5)/(3)x-1`