Question

graph the following features: - y-intercept = 2 - slope = $-\frac{6}{5}$

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. We are given that the $y$ - intercept $b = 2$ and the slope $m=-\frac{6}{5}$. So the equation of the line is $y=-\frac{6}{5}x + 2$.

Step2: Plot the y - intercept

The $y$ - intercept is the point where the line crosses the $y$ - axis. When $x = 0$, $y=2$. So we plot the point $(0,2)$ on the coordinate plane.

Step3: Use the slope to find another point

The slope $m =-\frac{6}{5}$ can be thought of as $\frac{\text{rise}}{\text{run}}=\frac{- 6}{5}$. This means that from the point $(0,2)$, we can move down 6 units (because the rise is - 6) and then move to the right 5 units (because the run is 5). So starting from $(0,2)$, moving down 6 units gives us a $y$ - coordinate of $2-6=-4$, and moving right 5 units gives us an $x$ - coordinate of $0 + 5=5$. So the new point is $(5,-4)$. We can also move up 6 units and left 5 units (since $\frac{-6}{5}=\frac{6}{-5}$). Starting from $(0,2)$, moving up 6 units gives $y = 2+6 = 8$ and moving left 5 units gives $x=0 - 5=-5$, so the point $(-5,8)$ is also on the line.

Step4: Draw the line

After plotting the points $(0,2)$ and $(5,-4)$ (or $(-5,8)$ and $(0,2)$), we draw a straight line passing through these points.

(Note: Since the question is about graphing, the final answer is the graph of the line with $y$ - intercept at $(0,2)$ and slope $-\frac{6}{5}$. If we were to write the equation, the equation is $y =-\frac{6}{5}x+2$)

Answer:

The equation of the line is $y =-\frac{6}{5}x + 2$, and the line is graphed by plotting the point $(0,2)$ and using the slope $-\frac{6}{5}$ to find another point (e.g., $(5,-4)$ or $(-5,8)$) and then drawing a straight line through these points.