13. \( -2 x+3 y=-6 \)

To tackle the equation \( -2x + 3y = -6 \) and express it in slope-intercept form (y = mx + b), let's isolate y. Adding \( 2x \) to both sides gives us \( 3y = 2x - 6 \). Next, divide every term by 3 to find \( y = \frac{2}{3}x - 2 \). This tells us that the slope is \( \frac{2}{3} \) and the y-intercept is -2, so the graph of this equation will be a straight line rising from left to right, crossing the y-axis at -2! When graphing, avoid common mistakes like confusing the slope with the y-intercept. Remember, the slope tells you how steep the line is and in which direction it tilts. If you recognize that you have the wrong slope or intercept, simply double-check your algebra and keep those numbers straight—precision is key!