The equation of a line is given below. \[ -4 x-2 y=-6 \] Find the slope and the \( y \)-intercept. Then use them to graph the line.

To find the slope and the \( y \)-intercept, first, we need to rewrite the equation in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the \( y \)-intercept. Starting with: \[ -4x - 2y = -6 \] Let's isolate \( y \): \[ -2y = 4x - 6 \] Now, divide each term by -2: \[ y = -2x + 3 \] From this equation, we can see that the slope \( m \) is -2 and the \( y \)-intercept \( b \) is 3. This means the line crosses the \( y \)-axis at (0, 3). When graphing, start at the \( y \)-intercept (0, 3). From there, use the slope of -2, which means for every step to the right (1 unit), move down 2 units. Connect these points to visualize your line, which slopes downwards from left to right! With this graphing technique, you'll master the art of line drawing in no time! An essential concept here is that slopes can indicate the steepness and direction of the line. Positive slopes rise from left to right, while negative slopes, like this one, descend. When graphing different lines, always double-check your intercepts. A common mistake is misplacing the \( y \)-intercept, which can skew the entire graph! Always plot the intercept first, and then utilize the slope to find additional points. Happy graphing!