Question

If the x- intercept is 2 and the y- intercept is -5 and the slope is 1/3. Write in equation in slope intercept form and standard form.

Answer 1

• The equation in slope-intercept form is

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

• The equation in the standard form will be:

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

Explanation:

• The x-intercept is obtained when we set the value y=0

As the x-intercept is 2, therefore the point representing

the x-intercept will be: (2, 0)

• The y-intercept is obtained when we set the value x=0

As the y-intercept is -5, therefore the point representing

the y-intercept will be: (0, -5)

So we get the two points

(2, 0)

(0, -5)

Finding the slope between (2, 0) and (0, -5)

`\left(x_1,\:y_1\right)=\left(2,\:0\right),\:\left(x_2,\:y_2\right)=\left(0,\:-5\right)`

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

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

`m=(5)/(2)`

Using the point-slope form of the line equation

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

Here m is the slope

substituting the values m = 5/2 and the point (2, 0)

`y-0=(5)/(2)\left(x-2\right)`

so writing the equation in slope-intercept form

As we know that the slope-intercept form is

`y=mx+b`

here

• m = gradient or slop

• b = y-intercept

so

`y=(5)/(2)\left(x-2\right)`

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

Hence, the equation in slope-intercept form is

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

Writing the equation in the standard form form

As we know that the equation in the standard form is

`Ax+By=C`

where x and y are variables and A, B and C are constants

As we already know the equation in slope-intercept form

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

so the equation in the standard form will be:

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