Question

Here’s a graph of linear function. Write the equation that describes the function.

Express it in slope-intercept form

Answer 1

Answer:
`y=(2)/(3)x+3`

Explanation:

From the graph, we observe that the line intersects the y-axis at y=3. So, the y-intercept of the line is c=3.

Let m be the slope of the line. Then, the equation of the line in the slope-intercept form is:

`y=mx+c\\\therefore y=mx+3 --- (1)`

Since the line contains the point (x,y)=(3,5), so substitute x=3 and y=5

into (1):

`5=3m+3\\3m=5-3\\3m=2\\m=(2)/(3)---(2)`

Substitute (2) into (1), and we get:

`y=(2)/(3)x+3`

Answer 2

y =2/3x + 3. 2/3 is from rise over run in this case m=2/3. And it crosses the y axis at 3 so b=3