Question

Write an equation for the line graphed.

Answer 1

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

Explanation:

The formula for equation of a line is
`y=mx+b` where m is the slope, b is the y-intercept, and (x,y) can represent any point on the line. We calculate the slope using
`(y_2-y_1)/(x_2-x_1)`. We are subtracting the y-coordinates in the numerator and the x-coordinates in the denominator.

`(0-2)/(3-0) = -(2)/(3)`

You can subtract the coordinates of your second point from your first point and you will get the same slope. Just be sure not to mix up the order.

Now that we have our slope, we can either pull the y-intercept off the graph; the line crosses the y-axis as y = 2, or we can solve our equation for the value of b.

We can pick any point on the line to solve for b. It is recommended to use one of the intercepts because either the x or y component will be zeroed out. I will use the point (0,2)

`y = mx + b\\y = -(2)/(3)x +b\\2 = (-(2)/(3))(0) + b\\b = 2`

Now we have all the parts of our equation in slope-intercept form.

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