Question

1. on the accompanying grid, draw the graph of the line whose slope is \\(\frac{2}{3}\\) and whose \\(y\\)-intercept is \\(-2\\).

Explanation:

Step1: Recall the slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept. Given that the slope $m=\frac{2}{3}$ and the $y$-intercept $b = - 2$, the equation of the line is $y=\frac{2}{3}x-2$.

Step2: Plot the y - intercept

The $y$-intercept is $-2$, so we start by plotting the point $(0,-2)$ on the coordinate grid. This is the point where the line crosses the $y$-axis.

Step3: Use the slope to find another point

The slope $m = \frac{2}{3}$ can be thought of as $\frac{\text{rise}}{\text{run}}=\frac{2}{3}$. From the point $(0,-2)$, we move up 2 units (because the numerator of the slope is 2, which represents the rise) and then move to the right 3 units (because the denominator of the slope is 3, which represents the run). This gives us the point $(0 + 3,-2+2)=(3,0)$.

Step4: Draw the line

Now that we have two points, $(0,-2)$ and $(3,0)$, we can draw a straight line passing through these two points. We can also find more points by continuing the pattern of rise over run (up 2, right 3 or down 2, left 3) to ensure the line is drawn accurately.

(Note: Since this is a graph - drawing problem, the final answer is the graph of the line $y = \frac{2}{3}x-2$ passing through the points $(0,-2)$ and $(3,0)$ (and other points obtained by the slope) on the given grid.)

Answer:

The graph of the line with slope $\frac{2}{3}$ and $y$-intercept $-2$ is drawn by first plotting the point $(0, - 2)$ (the $y$-intercept) and then using the slope $\frac{2}{3}$ (rise 2, run 3) to find another point (e.g., $(3,0)$) and drawing a straight line through these points.