graph the line that has a slope of 3 and includes the point (0, 5). 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 $m = 3$ and the line passes through the point $(0,5)$. The y - intercept $b$ is the value of $y$ when $x = 0$. So, when $x = 0$, $y=5$, which means $b = 5$. So the equation of the line is $y=3x + 5$.

Step2: Identify two points on the line

We already know one point is $(0,5)$ (the y - intercept). To find another point, we can use the slope. The slope $m=\frac{\text{rise}}{\text{run}}=3=\frac{3}{1}$. Starting from the point $(0,5)$, if we move 1 unit to the right (increase $x$ by 1, so $x = 0+1 = 1$) and 3 units up (increase $y$ by 3, so $y=5 + 3=8$), we get the point $(1,8)$.

Step3: Graph the line

Plot the points $(0,5)$ and $(1,8)$ (and other points if needed, for example, if we move 2 units to the right from $(0,5)$, $x = 2$, $y=3\times2 + 5=11$, but since the graph only goes up to $y = 10$, $(1,8)$ and $(0,5)$ are sufficient for this grid). Then draw a straight line through these points.

Answer:

To graph the line $y = 3x+5$:

• Plot the point $(0,5)$ (since when $x = 0$, $y = 5$).
• Use the slope $m = 3$ (rise of 3, run of 1) to find another point. From $(0,5)$, move 1 unit right (to $x = 1$) and 3 units up (to $y=8$) to get the point $(1,8)$.
• Draw a straight line through the points $(0,5)$ and $(1,8)$ (and extend it as needed).