Question

What is the equation of this graph?

Answer 1

Answer (assuming it is allowed to be written in slope-intercept form):

`y = -(2)/(3) x + 1`

Explanation:

When knowing a line's y-intercept and its slope, you can write its equation using slope-intercept form, or
`y = mx + b`.

1) First, find the slope of the line. Read the graph and look at the two points marked on the line - they are (0,1) and (3,-1). Use the slope formula
`(y_2-y_1)/(x_2-x_1)` , substitute the x and y values of those points, and solve:

`((-1)-(1))/((3)-(0)) \\= (-1-1)/(3-0) \\= (-2)/(3)`

Thus, the line's slope is
`-(2)/(3)`.

2) Now, use the slope-intercept formula,
`y = mx + b`, to write an equation. Substitute the
`m` and
`b` for real values.

The
`m` represents the slope, so substitute
`-(2)/(3)` in its place. The
`b` represents the y-value of the y-intercept, or the point at which the line crosses the y-axis. Looking at the graph, we can see that the line intersects the y-axis at (0,1). Thus, substitute 1 for
`b`. This gives the following equation and answer:

`y = -(2)/(3) x + 1`