Question

Write an equation of the line given an intercepts. Express in standard form.

1. x – intercept is 4 and y – intercept is 3.
2. x – intercept is -2 and y – intercept is 5.

Answer 1

Required equations in standard form are:

1. 3x+4y=12

2. -5x+2y = 10

Explanation:

Standard form of equation is given as:

`Ax+By = C`

1. x – intercept is 4 and y – intercept is 3.

The points will be:

(4,0) and (0,3)

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

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

Slope intercept form of line is:

`y = mx+b`

Putting the values of m and b(y-intercept)

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

Multiplying whole equation by 4

`4y = -3x+12\\3x+4y = 12`

2. x – intercept is -2 and y – intercept is 5

The points will be:

(-2,0) and (0,5)

Now

`m = (5-0)/(0+2)\\m = (5)/(2)`

Putting the values of m and b in slope intercept form

`y = (5)/(2)x+5`

Multiplying the equation by 2

`2y = 5x+10`

`-5x+2y=10`

Hence,

Required equations in standard form are:

1. 3x+4y=12

2. -5x+2y = 10