Question

graph this line using the slope and y-intercept: y = 9x + 1 click to select points on the graph.

Explanation:

Step1: Identify y-intercept

The equation is $y = 9x + 1$, in slope - intercept form $y=mx + b$ where $b$ is the y - intercept. So the y - intercept $b = 1$. This means the line crosses the y - axis at the point $(0,1)$.

Step2: Identify slope

The slope $m=9=\frac{9}{1}$. The slope is the rise over run, so from the y - intercept $(0,1)$, we can move up 9 units and right 1 unit to get the next point. So from $(0,1)$, moving up 9 (since $y$ increases by 9) and right 1 (since $x$ increases by 1) gives the point $(1,1 + 9)=(1,10)$. We can also move down 9 and left 1 from the y - intercept, but moving up and right is more straightforward for graphing in the positive direction.

Step3: Graph the points

First, plot the y - intercept $(0,1)$. Then plot the point $(1,10)$ (since when $x = 1$, $y=9(1)+1 = 10$). Then draw a straight line through these two points (and extend it). The current graph shown has a horizontal line at $y = 10$, but the correct line for $y=9x + 1$ should pass through $(0,1)$ and $(1,10)$ (and other points like $(2,19)$ etc., but for the given grid, $(0,1)$ and $(1,10)$ are key points to plot).

Answer:

To graph $y = 9x+1$:

1. Plot the y - intercept at $(0,1)$ (where the line crosses the y - axis, since when $x = 0$, $y=1$).
2. Use the slope $m = 9=\frac{9}{1}$. From $(0,1)$, move up 9 units and right 1 unit to get the point $(1,10)$ (since $y=9(1)+1 = 10$).
3. Draw a straight line through $(0,1)$ and $(1,10)$ (and extend it). The given graph in the problem is incorrect as it shows a horizontal line; the correct line should be a steeply increasing line passing through $(0,1)$ and $(1,10)$.