Question

3x - 2y = 16Please graph, show slope, and y intercept

Answer 1

In order to graph the equation, we need to find two ordered pairs that are solutions to the equation.

To do so, we can choose values for x and then calculate the corresponding values of y.

So, for x = 2 and x = 4, we have:

`\begin{gathered} x=2\colon \\ 6-2y=16 \\ 2y=-10 \\ y=-5 \\ \\ x=4\colon \\ 12-2y=16 \\ 2y=-4 \\ y=-2 \end{gathered}`

Now, graphing these points and the line that passes through them, we have:

The slope can be calculated using the two points in the formula:

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ m=(-2-(-5))/(4-2) \\ m=(-2+5)/(2) \\ m=(3)/(2) \end{gathered}`

The y-intercept can be calculated using x = 0 in the equation or looking where the graph intersects the y-axis:

`\begin{gathered} x=0\colon \\ -2y=16 \\ y=-8 \end{gathered}`

So the y-intercept is (0, -8).