Question

graph the line that has a slope of \\(\frac{1}{9}\\) and includes the point (0, 5). click to select points on the graph.

Explanation:

Step1: Identify the y-intercept

The point \((0, 5)\) is on the line, so the y-intercept \(b = 5\). The slope-intercept form of a line is \(y = mx + b\), where \(m\) is the slope. Here, \(m=\frac{1}{9}\), so the equation is \(y=\frac{1}{9}x + 5\).

Step2: Plot the y-intercept

First, plot the point \((0, 5)\) on the graph (this is where \(x = 0\), \(y = 5\)).

Step3: Use the slope to find another point

The slope \(\frac{1}{9}\) means "rise over run", so from \((0, 5)\), we move up 1 unit (rise) and right 9 units (run). This gives the point \((0 + 9, 5+ 1)=(9, 6)\). Alternatively, we can move down 1 and left 9 from \((0, 5)\) to get \((-9, 4)\), but since the graph shows \(x\) from 0 to 10, \((9, 6)\) is more appropriate.

Step4: Draw the line

Connect the points \((0, 5)\) and \((9, 6)\) (or other points found using the slope) to graph the line.

(Note: Since the task is to graph, the key steps are identifying the y - intercept, using the slope to find another point, and drawing the line through those points. The final "answer" here is the graph with the line passing through \((0, 5)\) and \((9, 6)\) (and other collinear points), but in the context of the problem's instruction to click points, the main points to select are \((0, 5)\) and \((9, 6)\) (or similar using the slope).)

Answer:

The line is graphed by plotting the point \((0, 5)\) and then using the slope \(\frac{1}{9}\) to find another point (e.g., \((9, 6)\)) and drawing a line through these points. The key points to select on the graph are \((0, 5)\) and \((9, 6)\) (or other points following the slope from \((0, 5)\)).