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: standard form slope: (drop - down with -2, 2.5, 5) question 1c

Explanation:

Step1: Recall Standard Form

The standard form of a linear equation is \(Ax + By = C\), where \(A\), \(B\), and \(C\) are integers, and \(A\geq0\). The given equation is \(5x - 2y = 10\), which matches the standard form (\(A = 5\), \(B=-2\), \(C = 10\)). So the form is standard form.

Step2: Find Slope from Standard Form

To find the slope, we can convert the standard form to slope - intercept form (\(y=mx + b\), where \(m\) is the slope).
Starting with \(5x-2y = 10\), we solve for \(y\):
Subtract \(5x\) from both sides: \(-2y=-5x + 10\).
Divide every term by \(-2\): \(y=\frac{-5}{-2}x+\frac{10}{-2}\), which simplifies to \(y = 2.5x-5\).
So the slope \(m = 2.5\).

Answer:

Form: standard form; Slope: \(2.5\)