Question

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

Answer 1

Answer:

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

Step-by-step 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)

$m=-\dfrac{5}{4}$

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

$y=-\dfrac{5}{4}x+5$

The standard form:

$Ax+By=C$

Convert:

$y=-\dfrac{5}{4}x+5$             multiply both sides by 4

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

$5x+4y=20$