Question

what is the equation of the line above?

a. \\(y = 3x - 2\\)
b. \\(y = \frac{1}{3}x + 2\\)
c. \\(y = \frac{1}{3}x - 2\\)
d. \\(y = -\frac{1}{3}x + 2\\)

Explanation:

Find the y-intercept from the graph

The line crosses the vertical \(y\)-axis at the point \((0, -2)\). Therefore, the \(y\)-intercept \(b\) is:

$$ b = -2 $$

Find the slope of the line

The line passes through the points \((0, -2)\) and \((3, -1)\). Using the slope formula:

$$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - (-2)}{3 - 0} = \frac{1}{3} $$

Write the equation in slope-intercept form

Substitute the slope \(m = \frac{1}{3}\) and \(y\)-intercept \(b = -2\) into the slope-intercept equation \(y = mx + b\):

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

Answer:

• A. \(y = 3x - 2\)
• B. \(y = \frac{1}{3}x + 2\)
• C. \(y = \frac{1}{3}x - 2\) (Correct answer)
• D. \(y = -\frac{1}{3}x + 2\)