Graph the equation. \( 3 x+4 y=-4 \)

To graph the equation \( 3x + 4y = -4 \), start by rearranging it into slope-intercept form, \( y = mx + b \). First, solve for \( y \): \[ 4y = -3x - 4 \] Now divide by 4: \[ y = -\frac{3}{4}x - 1 \] This reveals a slope of \(-\frac{3}{4}\) and a y-intercept of \(-1\) (the point (0, -1) on the y-axis). From the y-intercept, you can plot the point (0, -1). Next, use the slope to find another point: from (0, -1), go down 3 units and right 4 units to reach (4, -4). Plot this point and draw a straight line through them. Voila, your graph is complete! To ensure your line is accurate, you could take a moment to find the x-intercept as well. Set \(y = 0\) in the original equation to find where it intersects the x-axis: \[ 3x + 0 = -4 \] Thus, \(x = -\frac{4}{3}\) or approximately -1.33. Plotting this point along with the other two helps check your work for accuracy. Happy graphing!