Chapter 1.3, Problem 136AYU

To determine

To find: Can the equation of every line be written in slope-intercept form? Why?

Answer to Problem 136AYU

The first of the forms for a linear equation is slope-intercept form. Equations in slope-intercept form look like this:

$y=mx+b$

where $m$ is the slope of the line and $b$ is the $y\text{-intercept}$ of the line, or the $y\text{-coordinate}$ of the point at which the line crosses the $y\text{-axis}$.

To write an equation in slope-intercept form, given a graph of that equation, pick two points on the line and use them to find the slope. This is the value of $m$ in the equation. Next, find the coordinates of the $y\text{-intercept}$--this should be of the form $\left(0, b\right)$. The $y\text{-coordinate}$ is the value of $b$ in the equation.

My conclusion that the equation of every straight line can be written in the slope-intercept form.

Explanation of Solution

There are several forms that the equation of a line can take. They may look different, but they all describe the same line-a line can be described by many equations. All (linear) equations describing a particular line, however, are equivalent.

The first of the forms for a linear equation is slope-intercept form. Equations in slope-intercept form look like this:

$y=mx+b$

where $m$ is the slope of the line and $b$ is the $y\text{-intercept}$ of the line, or the $y\text{-coordinate}$ of the point at which the line crosses the $y\text{-axis}$.

To write an equation in slope-intercept form, given a graph of that equation, pick two points on the line and use them to find the slope. This is the value of $m$ in the equation. Next, find the coordinates of the $y\text{-intercept}$--this should be of the form $\left(0, b\right)$. The $y\text{-coordinate}$ is the value of $b$ in the equation.

My conclusion that the equation of every straight line can be written in the slope-intercept form.