Question

use the point-slope formula to write an equation of the line having the given conditions. write the answer in slope-intercept form (if possible).

passes through \\((0, -2)\\) and \\(m = \frac{2}{5}\\).

part 1 of 3
label \\((0, -2)\\) as \\((x_1, y_1)\\) and \\(m = \frac{2}{5}\\).
apply the point-slope formula given by \\(y - y_1 = m(x - x_1)\\).

part 2 of 3
substitute \\(x_1 = 0\\), \\(y_1 = -2\\), and \\(m = \frac{2}{5}\\).
\\(y - (-2) = \frac{2}{5}x - (0)\\)

part 3 of 3
simplifying, the slope-intercept form of the line is \\(y = \\) .

Explanation:

Step1: Identify the substituted equation

$$y - (-2) = \frac{2}{5}(x - 0)$$

Step2: Simplify both sides

$$y + 2 = \frac{2}{5}x$$

Step3: Solve for y

$$y = \frac{2}{5}x - 2$$

Answer:

\(y = \frac{2}{5}x - 2\)