Question

The line above goes through points (-4,0) and (0,3). What is the equation of the line?

Answer 1

The equation of line going through points (-4, 0) and (0, 3) is
`y = (3)/(4)x + 3`

Solution:

Given that line above goes through points (-4,0) and (0,3)

To find: equation of line

The equation of line passing through two points
`(x_1 , y_1)` and
`(x_2, y_2)` is given as:

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

Where "m" is the slope of line

The slope of line is given as:

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

Here for the given points (-4, 0) and (0, 3) we have:

`x_1 = -4 ; y_1 = 0 ; x_2 = 0 ; y_2 = 3`

Substituting the given values in slope formula,

`m=(3-0)/(0-(-4))=(3)/(4)`

Thus slope of line
`m = (3)/(4)`

Now substitute "m" into equation of line

Thus the required equation of line is:

`y - y_1 = m(x - x_1)\\\\y - 0 = (3)/(4)(x - (-4))\\\\y = (3)/(4)(x + 4)\\\\y = (3)/(4)x + 3`

Thus the required equation of line is found