Problem 22 - College Algebra Essentials

Question

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope \(=\frac{1}{3},\) passing through the origin

Step-by-Step Solution

Answer

The point-slope form of the equation is: \(y = \frac{1}{3}x\), and the slope-intercept form of the equation is: \(y = \frac{1}{3}x\).

Step 1: Write point-slope equation

Start by writing down the point-slope form, which looks like this: \(y - y_1 = m(x - x_1)\) . For this specific problem, 'm' is the slope and ( \(x_1, y_1)\) is the given point through which the line passes. Substituting the slope and the point (0,0) into the equation we get: \(y - 0 = \frac{1}{3}(x - 0)\) which simplifies to: \(y = \frac{1}{3}x\).

Step 2: Write slope-intercept equation

The slope-intercept form of the equation is \(y = mx + b\), where 'm' is the slope and 'b' is the y-intercept. We know our slope 'm' is \(\frac{1}{3}\), and because our line passes through the origin, our y-intercept 'b' is 0. We substitute these values back into our equation to get: \(y = \frac{1}{3}x + 0\) which simplifies to \(y = \frac{1}{3}x\).