Question

Use the graph to write a linear function that relates y to x.

Answer 1

The basic structure of a linear function is y=mx+b (or +c, depending on your schools curriculum)

We need to find the slope (m), and the y-intercept (b/c)

To find the slope you can pick two random points, say (2,2) and (0,1)

The formula for the slope is this: m= y1-y2 / x1-x2

So if we substitute the points in, we get 2-1 / 2-0 = 1/2

Knowing the slope, it can be substituted into to the equation: y=1/2x + b

Then, if you notice the second point- (0,1), it’s the y-intercept. The y coordinate there is 1.

To check if this is correct, a random coordinate set can be picked and substituted in to find b.

y= 1/2x + b
2 = 1/2 *2 + b
2 = 1 + b
2-1=b
1=b

Therefore, the final linear function is y = 1/2 x + 1