A graph of an additive pattern contains the points (3,16) and (8,21) . What expression does the graph represent?(1 point)
x+
To find the expression represented by the graph, we need to determine the relationship between the x and y values. The graph is a straight line, indicating a linear relationship.
To find the equation of the line, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope of the line.
Let's use the point (3,16) as our reference point:
y - 16 = m(x - 3)
To find the slope, we can use the second point (8,21):
m = (y2 - y1) / (x2 - x1) = (21 - 16) / (8 - 3) = 5 / 5 = 1
Now we have the slope, and we can substitute it back into the equation:
y - 16 = 1(x - 3)
y - 16 = x - 3
Finally, rearranging the equation to isolate y:
y = x - 3 + 16
y = x + 13
Therefore, the expression represented by the graph is: x + 13.