Write the equation of the line in fully simplified slope-intercept form.

Mathematics

2 answers:

Leya [2.2K]3 years ago

4 0

Answer:

$y = -\frac{1}{6}x +2$

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, $\frac{y_2-y_1}{x_2-x_1}$ . 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:

$\frac{(1)-(2)}{(6)-(0)} \\= \frac{1-2}{6-0}\\= \frac{-1}{6}$

Thus, $-\frac{1}{6}$ 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 $-\frac{1}{6}$ for m. This will give the following equation of the line in slope-intercept format:

$y = -\frac{1}{6}x +2$