Question

What is the equation of this graph?

Answer 1

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

$y = -\frac{2}{3} x + 1$

Step-by-step 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 $\frac{y_2-y_1}{x_2-x_1}$ , substitute the x and y values of those points, and solve:

$\frac{(-1)-(1)}{(3)-(0)} \\= \frac{-1-1}{3-0} \\= \frac{-2}{3}$

Thus, the line's slope is $-\frac{2}{3}$.

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 $-\frac{2}{3}$  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:

$y = -\frac{2}{3} x + 1$