Answer:
[tex]y = -\frac{1}{6}x +2[/tex]
Step-by-step explanation:
To write an equation into slope-intercept form, or y = mx + b format, we need to find the y-intercept of the line and its slope and substitute values for m and b.
1) First, find the y-intercept. The y-intercept is the point at which the line intersects the y-axis. Reading the graph, we can see that the line passes the y-axis at the point (0,2), thus that is the y-intercept.
2) Next, find the slope. Pick out two points on the graph to use for the slope formula, [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]. I chose to work with (0,2) and (6,1). Now, substitute the two points' x and y values into the formula appropriately and solve:
[tex]\frac{(1)-(2)}{(6)-(0)} \\= \frac{1-2}{6-0}\\= \frac{-1}{6}[/tex]
Thus, [tex]-\frac{1}{6}[/tex] is the slope.
3) Now, substitute the calculated values into the y = mx + b format. The b represents y-value of the y-intercept. The y-intercept is (0,2), thus substitute 2 for b. The coefficient of the x term, or m, represents the slope, thus substitute [tex]-\frac{1}{6}[/tex] for m. This will give the following equation of the line in slope-intercept format:
[tex]y = -\frac{1}{6}x +2[/tex]
