graph this line using the slope and y - intercept: y = -\\frac{1}{4}x + 2. click to select points on the…

Explanation:

Step1: Identify the slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Given $y=-\frac{1}{4}x + 2$, the slope $m=-\frac{1}{4}$ and the y - intercept $b = 2$.

Step2: Find the y - intercept point

The y - intercept is the point where the line crosses the y - axis. When $x = 0$, $y=-\frac{1}{4}(0)+2=2$. So the y - intercept point is $(0,2)$.

Step3: Use the slope to find another point

The slope $m =-\frac{1}{4}=\frac{\Delta y}{\Delta x}$. Starting from the point $(0,2)$, if we move 4 units to the right ($\Delta x=4$), then $\Delta y=- 1$. So another point is $(0 + 4,2-1)=(4,1)$.

Step4: Plot the points and draw the line

Plot the points $(0,2)$ and $(4,1)$ on the coordinate plane and draw a straight line passing through them.

Answer:

Plot the points $(0,2)$ and $(4,1)$ and draw a straight - line through them.