Question

graph the following features: - slope = \\(\frac{5}{3}\\) - y-intercept = \\(-3\\)

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 $m=\frac{5}{3}$ and the y - intercept $b = - 3$, the equation of the line is $y=\frac{5}{3}x-3$.

Step2: Plot the y - intercept

The y - intercept is the point where the line crosses the y - axis. When $x = 0$, $y=-3$. So we plot the point $(0,-3)$ on the coordinate plane.

Step3: Use the slope to find another point

The slope $m=\frac{5}{3}$ can be thought of as $\frac{\text{rise}}{\text{run}}=\frac{5}{3}$. This means that from the point $(0, - 3)$, we can move up 5 units (because the numerator of the slope is positive) and then move to the right 3 units (because the denominator of the slope is positive).
Starting from $(0,-3)$:

• Rise: $y$ - coordinate changes by $+ 5$: $-3 + 5=2$
• Run: $x$ - coordinate changes by $+3$: $0 + 3 = 3$

So we get the point $(3,2)$. We can also move down 5 units and left 3 units from $(0,-3)$ (since $\frac{- 5}{-3}=\frac{5}{3}$) to get another point, for example, $(-3,-8)$ (starting from $(0,-3)$, $x=0 - 3=-3$, $y=-3-5 = - 8$).

Step4: Draw the line

After plotting the y - intercept $(0,-3)$ and at least one other point (e.g., $(3,2)$ or $(-3,-8)$), we can draw a straight line passing through these points.

(Note: Since the problem is about graphing, the final answer is the graph of the line with equation $y = \frac{5}{3}x-3$ passing through $(0,-3)$ and other points determined by the slope.)

Answer:

The graph is a straight line with a y - intercept at $(0, - 3)$ and a slope of $\frac{5}{3}$, passing through points like $(3,2)$ (obtained by moving 3 units right and 5 units up from the y - intercept) and $(-3,-8)$ (obtained by moving 3 units left and 5 units down from the y - intercept), and following the equation $y=\frac{5}{3}x - 3$.