Question

graph the line that has a slope of 5 and includes the point (0, 2). click to select points on the graph.

Explanation:

Step1: Recall the slope-intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know that the slope $m = 5$ and the line passes through the point $(0,2)$. The y - intercept $b$ is the value of $y$ when $x = 0$, so when $x = 0,y = 2$, which means $b=2$. So the equation of the line is $y=5x + 2$.

Step2: Identify the y - intercept point

The y - intercept is at $(0,2)$, so we can plot this point first.

Step3: Use the slope to find another point

The slope $m=\frac{\text{rise}}{\text{run}}=5=\frac{5}{1}$. From the point $(0,2)$, if we move 1 unit to the right (run = 1) and 5 units up (rise = 5), we get the point $(0 + 1,2+5)=(1,7)$. We can also move in the opposite direction: from $(0,2)$, move 1 unit to the left (run=- 1) and 5 units down (rise = - 5) to get the point $(- 1,-3)$, but since our graph has non - negative x - values shown, we focus on the point $(1,7)$ and $(0,2)$ for graphing.

To graph the line, we plot the points $(0,2)$ and $(1,7)$ (and other points obtained by using the slope) and draw a straight line through them. The key points to plot are $(0,2)$ (the y - intercept) and then using the slope of 5 (for every 1 unit increase in $x$, $y$ increases by 5) to find additional points like $(1,7),(2,12)$ (but 12 is above the given graph's y - axis range, so $(0,2)$ and $(1,7)$ are sufficient for the given grid).

Answer:

To graph the line:

1. Plot the point \((0, 2)\) (the y - intercept).
2. Use the slope \(m = 5=\frac{5}{1}\): from \((0,2)\), move 1 unit right (to \(x = 1\)) and 5 units up (to \(y=2 + 5=7\)) to plot the point \((1,7)\).
3. Draw a straight line through the points \((0, 2)\) and \((1, 7)\) (and extend it as needed).