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Chapter 2: Problem 22

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

Short Answer

Expert verified
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 by step solution

01

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: \(y = \frac{1}{3}x\).
02

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 \(y = \frac{1}{3}x\).

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