Question

graph the line using the slope and y-intercept.
graph the line through the point (0, 1), having a slope of \\(\frac{5}{6}\\).

Explanation:

Step 1: Identify the y - intercept

The point \((0,1)\) is the y - intercept because when \(x = 0\), \(y=1\). So we start by plotting the point \((0,1)\) on the coordinate plane.

Step 2: Use the slope to find another point

The slope \(m=\frac{5}{6}\), which is in the form \(\frac{\text{rise}}{\text{run}}\). The rise is the change in \(y\) and the run is the change in \(x\). From the point \((0,1)\), we move up (since the numerator of the slope is positive) 5 units (because the rise is 5) and then move to the right (since the denominator of the slope is positive) 6 units. So from \((0,1)\), adding 5 to the \(y\) - coordinate and 6 to the \(x\) - coordinate, we get the new point \((0 + 6,1+5)=(6,6)\).

Step 3: Draw the line

Now that we have two points \((0,1)\) and \((6,6)\), we can draw a straight line passing through these two points. This line represents the equation of the line with y - intercept \((0,1)\) and slope \(\frac{5}{6}\).

(Note: Since this is a graphing problem, the final answer is the graph of the line passing through \((0,1)\) and \((6,6)\) (or other points found using the slope from \((0,1)\)) with a slope of \(\frac{5}{6}\).)

Answer:

The line is graphed by first plotting the y - intercept \((0,1)\), then using the slope \(\frac{5}{6}\) (rise = 5, run = 6) to find another point (e.g., \((6,6)\)) and drawing a straight line through these points.