Question

Find the slope and the \(y\) -intercept of the graph of the equation. Then graph the equation. $$ -2 y-3 x=6 $$

Short answer

The slope of the line is -1.5 and the y-intercept is -3. In the graphical representation, the line passes through the point (0, -3) on the y-axis and proceeds downward as the slope is negative.

Step-by-step solution

Rewrite the equation to slope-intercept form

To convert \(-2y - 3x = 6\) into slope-intercept form, first solve for \(y\). First, rearrange the equation to get \(-2y = 3x + 6\). Divide every term by -2 to isolate \(y\). So, \(y = -1.5x -3\).

Identify the slope and y-intercept

The slope-intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. Comparing this to our given equation, we can see that \(m = -1.5\) and \(b = -3\). So, the slope of the line is -1.5 and the y-intercept is -3.

Graph the equation

Begin by marking the y-intercept (0, -3) on the y-axis. Since the slope is -1.5, move one unit down and 1.5 units to the right from the y-intercept to get the next point (1.5, -4). Draw a line through these two points to graph the equation.