Question

Write an equation of the line in slope-intercept form and standard form

Answer 1

Given:

The graph of a line.

To find:

The equation of the line in slope-intercept form and standard form.

Solution:

From the given graph it is clear that the line passes through the points (0,-3) and (4,0). So, the slope of the line is:

`m=(y_2-y_1)/(x_2-x_1)`

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

`m=(3)/(4)`

The slope intercept form of a line is:

`y=mx+b`

Where, m is the slope and b is the y-intercept.

The y-intercept of the given line is -3 and the slope is
`(3)/(4)`. So, the slope intercept form of the line is:

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

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

Standard form of a line is:

`Ax+By=C`

Multiply both sides by 4 in (i).

`4y=3x-12`

`12=3x-4y`

`3x-4y=12`

Therefore, the slope intercept form of the line is
`y=(3)/(4)x-3` and the standard form of the line is
`3x-4y=12`.