Questions: Slope = 2/3, passing through the origin Write an equation for the line in point-slope form. (Simplify your answer. Use integers or fractions for any numbers in the

$Slope = 2/3, passing through the origin Write an equation for the line in point-slope form. (Simplify your answer. Use integers or fractions for any numbers in the$

Transcript text: Slope $=\frac{2}{3}$, passing through the origin Write an equation for the line in point-slope form. $\square$ (Simplify your answer. Use integers or fractions for any numbers in the

Solution

Solution Steps

To write the equation of a line in point-slope form, we use the formula $ y - y_1 = m(x - x_1) $, where $ m $ is the slope and $ (x_1, y_1) $ is a point on the line. Given that the slope $ m = \frac{2}{3} $ and the line passes through the origin $(0, 0)$, we can substitute these values into the formula.

Step 1: Identify the Given Values

We are given the slope $ m = \frac{2}{3} $ and the point $(0, 0)$ through which the line passes.

Step 2: Substitute Values into Point-Slope Form

The point-slope form of a line is given by: \[ y - y_1 = m(x - x_1) \] Substituting $ m = \frac{2}{3} $, $ x_1 = 0 $, and $ y_1 = 0 $ into the equation, we get: \[ y - 0 = \frac{2}{3}(x - 0) \]

Step 3: Simplify the Equation

Simplifying the equation, we obtain: \[ y = \frac{2}{3}x \]