Question

What is the equation of the line? Write in standard form. (4,5).

Answer 1

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

Explanation:

The equation of a line in slope-intercept form:

`y=mx+b`

m - slope

b - y-intercept → (0, b)

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

Therefore we have the equation:

`y=mx+5`

Put the coordinates of x-intercept to the equation:

`0=4m+5` subtract 4m from both sides

`-4m=5` divide both sides by (-4)

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

Finally we have the equation of a line if slope-intercept form:

`y=-(5)/(4)x+5`

The standard form:

`Ax+By=C`

Convert:

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

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

`5x+4y=20`