What is the equation that has a x intercept at 2,0 and y intercept at 0,4

Answer 1

y intercept is (0,4) or y = 4

x intercept is (2,0)

slope = "rise over run" = (4-0)/(0-2) = -2

in slope intercept form the equation is y=mx+b where m=-2, b=4

y =-2x + 4

or

2x + y = 4 in standard form

that's the linear equation with the given intercepts

but there are an infinite number of other non-linear equations with those intercepts

a quadratic equation with those intercepts is

y = (x-2)^2, an upward opening parabola with vertex & minimum point (2,0)

or

y = x^2 - 4x + 4

there are endless more non-linear equations that also have the same two intercepts.

Answer 2

solve for slope, y = -2x + 4