# What is the slope and y-intercept of this line y = x – 3?

Mar 12, 2018

See a solution process below:

#### Explanation:

This equation is in slope-intercept form. The slope-intercept form of a linear equation is: $y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$

Where $\textcolor{red}{m}$ is the slope and $\textcolor{b l u e}{b}$ is the y-intercept value.

$y = \textcolor{red}{m} x - \textcolor{b l u e}{3}$

$y = \textcolor{red}{1} x + \textcolor{b l u e}{- 3}$

Therefore:

• The slope is: $\textcolor{red}{m = 1}$

• The $y$-intercept is: $\textcolor{b l u e}{b = - 3}$ or $\left(0 , \textcolor{b l u e}{- 3}\right)$

Mar 12, 2018

slope$= 1$ and y-intercept$= - 3$

#### Explanation:

The slope of a slope-intercept equation is also the coefficient of $x$,

slope$= 1$

The y-intercept of a slope-intercept equation is also the constant,

y-intercept$= - 3$

There you go!

Mar 12, 2018

$y = x - 3 \implies \frac{\mathrm{dy}}{\mathrm{dx}} =$1=>slope,$m = 1$
Take,$x = 0 \implies y = 0 - 3 \implies y = - 3 =$Y-intercept

#### Explanation:

If the equation of the line is $a x + b y + c = 0$,then,
slope of line $m = - \frac{a}{b}$and Y-intercept $= - \frac{c}{b}$
$y = x - 3 \implies x - y - 3 = 0 \implies a = 1 , b = - 1 , c = - 3 \implies$
slope of line $m = - \frac{1}{- 1} = 1$
Y-intercept $= - \frac{- 3}{- 1} = - 3$