Question

determine the form of the equation, then determine the slope, x-intercept, and y-intercept. 5x - 2y = 10 > select from the drop-down menus to correctly complete the statement. form: slope: general form standard form factored form

Explanation:

Step1: Identify the form

The equation \(5x - 2y = 10\) is in standard form (since standard form of a linear equation is \(Ax + By = C\), here \(A = 5\), \(B=- 2\), \(C = 10\)). But let's check the drop - down. Wait, maybe first convert to slope - intercept form \(y=mx + b\) to find slope.
Solve \(5x-2y = 10\) for \(y\):
Subtract \(5x\) from both sides: \(-2y=-5x + 10\)
Divide both sides by \(- 2\): \(y=\frac{5}{2}x-5\)

Step2: Determine the form of the equation

The given equation \(5x - 2y=10\) is in standard form (standard form of a linear equation is \(Ax+By = C\), where \(A\), \(B\), \(C\) are integers and \(A\geq0\)). Looking at the drop - down menu for the form, if we consider the options: general form is \(Ax + By+C = 0\) (our equation can be written as \(5x-2y - 10=0\), but the original is \(5x - 2y = 10\) which is standard form. Wait, maybe the first drop - down: the equation \(5x-2y = 10\) is in standard form. But let's proceed to find slope, x - intercept, y - intercept.
Slope: From \(y=\frac{5}{2}x-5\), the slope \(m=\frac{5}{2}\)
x - intercept: Set \(y = 0\) in \(5x-2y = 10\), then \(5x=10\), so \(x = 2\)
y - intercept: From \(y=\frac{5}{2}x-5\), when \(x = 0\), \(y=-5\), or set \(x = 0\) in \(5x-2y = 10\), we get \(-2y=10\), \(y=-5\)

But first, for the form: The equation \(5x - 2y = 10\) is in standard form. If the drop - down has standard form as an option (from the image, the slope - form drop - down? Wait, the first drop - down (form) options: let's re - check. The image shows a drop - down with general form, standard form, factored form. The equation \(5x-2y = 10\) is in standard form (standard form of linear equation is \(Ax + By=C\)).

Answer:

Form: standard form; Slope: \(\frac{5}{2}\); x - intercept: \(2\); y - intercept: \(-5\)

(If we consider the drop - down for form: standard form. Slope: \(\frac{5}{2}\), x - intercept: \(2\), y - intercept: \(-5\))