Recall that in order to find the slope of a line we just need two points on the line of the form (x, y)
And the slope will be determined by the formula:
slope = (y2 - y1) / (x2 - x1)
in our case, we can find two very clearly determined points in the intersection the line makes with the grid at the points: (5, 120) and (15, 180)
Therefore the slope becomes:
slope = (280 - 120) / (15 - 5) = 160 / 10 = 16 miles/hour
Notice that the units of the slope are miles per hour since the y values represent miles, and the x values represent time in hours.
We notice also that at time ZERO (0 hours) the person is not at the origin, but at 90 miles from the origin.
Therefore the equation that represents this graph in point slope form can be written as:
y = 16 x + 90
where y is the distance from the origin in miles, and x is the elapsed time in hours.
This representation tells us that the person is travelling at a constant speed of 16 miles per hour.
The unit rate is 16 miles per one hour
If one wants to plot this line using the point-slope form, one needs to use the value of the slope (16 mi/h) and one point where the line goes. We can pick for example the point (0,90) which is where the line intersects the y axis, and the location the person is at time zero.
Once you mark that point on the plane , then you move to the right ONE unit (for ONE hour), and 16 units up (for the 16 miles covered during that hour, and then you have a second point created that fashion. Then, you join these points.
I will be marking what I just told you in the graph you provided. Give me a few minutes to draw the process.
Notice the point where we start (in orange), then we move to the right 1 hour and up the equivalent to 16 miles, and we get a new point (in red) that tells us the location "y value" at that time. This new point is the starting value for the next point, which again is obtained by moving to the right one hour and up anither 16 units (these steps are marked with green segments). The nex point we get with this procedure is the one depicted in light blue.
At the end you join the points you created this way with a straight line to complete the graph.