Answer:
y = 4/3x +2
Explanation:
You want a linear function that relates y to x as shown in the graph.
Linear function
A linear function can be written in slope-intercept form as ...
y = mx + b . . . . . . line with slope m and y-intercept b
Slope
The slope is the ratio "rise"/"run". Each of these can be found by counting grid squares where the line crosses grid points.
The point on the y-axis is on a grid intersection, and the point at the top with coordinates (6, 10) is also on a grid intersection. There are 4 vertical squares between these points, and 3 horizontal squares. This means the slope is ...
m = rise/run = 4/3
Y-intercept
The line crosses the y-axis on the grid line that would be labeled 2. So, b=2 in our equation of the line.
Function
The desired linear function is ...
y = mx +b
y = 4/3x +2
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Additional comment
You can also find the slope between two points using the slope formula:
m = (y2 -y1)/(x2 -x1)
For points (0, 2) and (6, 10), the slope is ...
m = (10 -2)/(6 -0) = 8/6 = 4/3 . . . . . . as above
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