Answer:
[tex]\large\boxed{5x+4y=20}[/tex]
Step-by-step explanation:
The equation of a line in slope-intercept form:
[tex]y=mx+b[/tex]
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:
[tex]y=mx+5[/tex]
Put the coordinates of x-intercept to the equation:
[tex]0=4m+5[/tex] subtract 4m from both sides
[tex]-4m=5[/tex] divide both sides by (-4)
[tex]m=-\dfrac{5}{4}[/tex]
Finally we have the equation of a line if slope-intercept form:
[tex]y=-\dfrac{5}{4}x+5[/tex]
The standard form:
[tex]Ax+By=C[/tex]
Convert:
[tex]y=-\dfrac{5}{4}x+5[/tex] multiply both sides by 4
[tex]4y=-5x+20[/tex] add 5x to both sides
[tex]5x+4y=20[/tex]
