Answer (assuming it is allowed to be written in slope-intercept form):
[tex]y = -\frac{2}{3} x + 1[/tex]
Step-by-step explanation:
When knowing a line's y-intercept and its slope, you can write its equation using slope-intercept form, or [tex]y = mx + b[/tex].
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 [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] , substitute the x and y values of those points, and solve:
[tex]\frac{(-1)-(1)}{(3)-(0)} \\= \frac{-1-1}{3-0} \\= \frac{-2}{3}[/tex]
Thus, the line's slope is [tex]-\frac{2}{3}[/tex].
2) Now, use the slope-intercept formula, [tex]y = mx + b[/tex], to write an equation. Substitute the [tex]m[/tex] and [tex]b[/tex] for real values.
The [tex]m[/tex] represents the slope, so substitute [tex]-\frac{2}{3}[/tex] in its place. The [tex]b[/tex] 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 [tex]b[/tex]. This gives the following equation and answer:
[tex]y = -\frac{2}{3} x + 1[/tex]
