Question

Determine the standard from of the equation of the line that pasees though (0,5 and (4,0)

Answer 1

The standard form:

`Ax+By=C`

The slope-intercept form:

`y=mx+b`

m - slope

b - y-intercept → (0, b).

The formula of a slope

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

We have the points (4, 0) and (0, 5) → y-intercept → b = 5.

Calculate the slope:

`m=(5-0)/(0-4)=(5)/(-4)=-(5)/(4)`

Therefore we have:

`y=-(5)/(4)x+5` multiply both sides by 4

`4y=-5x+20` add 5x to both sides

`\boxed{5x+4y=20}`

Answer 2

5x+ 4y =20

Explanation:

Slope = (y2-y1)/(x2-x1)

= (0-5)/(4-0)

= -5/4

We know the slope = -5/4 and the y intercept (x=0) y= 5

The euqation in slope intercept form is

y=mx+b whre m is the slope and b is the y intercept

y = -5/4 x +5

Multiply each side by 4 to get rid of the fraction

4y = 4*-5/4x + 5*4

4y = -5x+20

Add 5x to each side

5x+4y = 5x-5x+20

5x+ 4y =20

This is the standard form of a line

Ax + By =C