We are asked to find the slope of a line that is parallel to the line on the graph.
Recall that parallel lines have the same slope, so we will find the slope of the given line. To do this, let's first determine two lattice points on the line.
The slope of a line passing through two points is defined as the ratio of the vertical change (the rise) to the horizontal change between the points — the run.
Starting with the point on the left, we need to move 3 steps horizontally in the positive direction and 1 unit vertically in the positive direction to reach the other point.
Slope=Rise/Run ⇒ Slope=1/3
Therefore, the slope of the line on the graph is 13. Since a line that is parallel to the line on the graph has the same slope, the correct choice is option H.
Alternative Solution
Alternative solution
We can also algebraically calculate the slope m of a line passing through two points (x_1,y_1) and (x_2,y_2) using the Slope Formula.
m=y_2-y_1/x_2-x_1
First, we need to determine two lattice points on the given line.
Let's now substitute the points ( 0,2) and ( 3,3) into the Slope Formula and solve it for m.
