Question

how would you graph the following line?
y = -3x + 5
first, you would select. the y-intercept here is select. then you would select. the slope here is select. to plot the slope, you would move from your y-intercept select.
lastly, you would connect the points with a straight line with arrows to show that it goes on forever in both directions.

Explanation:

Step1: Identify the y - intercept

The equation of a line in slope - intercept form is $y = mx + b$, where $b$ is the y - intercept. For the line $y=-3x + 5$, we can see that when $x = 0$, $y=b$. So first, we would plot the y - intercept. The y - intercept ($b$) here is $5$ (since in $y=-3x + 5$, $b = 5$).

Step2: Identify the slope

The slope ($m$) in the slope - intercept form $y=mx + b$ is the coefficient of $x$. For $y=-3x + 5$, the slope $m=-3$. Then we would use the slope to find another point. To plot the slope, since the slope is $\frac{\text{rise}}{\text{run}}=-3=\frac{- 3}{1}$, you would move from your y - intercept 3 units down (because the rise is - 3) and 1 unit to the right (because the run is 1), or 3 units up and 1 unit to the left (since $\frac{-3}{1}=\frac{3}{-1}$).

For the first "Select" (what to do first): The first step to graph a line in slope - intercept form is to plot the y - intercept. So the first "Select" should be "plot the y - intercept".

For the second "Select" (y - intercept value): The y - intercept is $5$, so the second "Select" should be $5$.

For the third "Select" (what to do next): After plotting the y - intercept, we use the slope to find another point. So the third "Select" should be "use the slope to find another point".

For the fourth "Select" (slope value): The slope is $-3$, so the fourth "Select" should be $-3$.

For the fifth "Select" (how to move for slope): Since the slope is $-3=\frac{-3}{1}$, we move 3 units down and 1 unit to the right (or 3 units up and 1 unit to the left). A common way is 3 units down and 1 unit to the right, so the fifth "Select" could be "3 units down and 1 unit to the right" (or the equivalent for the negative slope interpretation).

Answer:

First "Select": plot the y - intercept
Second "Select": 5
Third "Select": use the slope to find another point
Fourth "Select": - 3
Fifth "Select": 3 units down and 1 unit to the right (or other correct slope - based movement like 3 units up and 1 unit to the left)