(a) Write the equation in slope-intercept form, and determine the slope and \( y \)-intercept. (b) Graph the equation using the slope and \( y \)-intercept. \[ -5 x+2 y=-10 \] Part: \( 0 / 2 \) \( \square \) Part 1 of 2 The slope is \( \square \) . The \( y \)-intercept is \( \square \) . \( \square \) D. The equation written in slope-intercept form is \( \square \) . Skip Part Check

First, let's rewrite the equation in slope-intercept form (y = mx + b). Start with the equation \(-5x + 2y = -10\). To isolate \(y\), add \(5x\) to both sides, yielding \(2y = 5x - 10\). Next, divide the entire equation by 2 to solve for \(y\): \(y = \frac{5}{2}x - 5\). From this, we can see that the slope \(m\) is \(\frac{5}{2}\) and the \(y\)-intercept \(b\) is \(-5\). Now, grab your graphing tools! To plot the line, start at the \(y\)-intercept, which is the point (0, -5). From there, use the slope \(\frac{5}{2}\) to rise 5 units and run 2 units to the right, landing at the point (2, 0). Connect these dots for the straight line representing the equation. Voilà! You’ve got your graph! The slope is \(\frac{5}{2}\). The \(y\)-intercept is \(-5\). The equation written in slope-intercept form is \(y = \frac{5}{2}x - 5\). Did you know that the slope of a line describes its steepness and direction? In this case, a positive slope like \(\frac{5}{2}\) means the line climbs from left to right, making it perfect for representing trends that increase over time! Also, understanding how to manipulate equations into different forms is crucial in math and beyond! Slope-intercept form is particularly useful because it allows for quick determinations of momentums in data, whether you're projecting sales, studying physics, or even navigating a hike!