# How do you graph x-y=1 ?

Jul 29, 2018

Determine the x- and y-intercepts, plot them, and draw a straight line through the point.

#### Explanation:

Graph:

$x - y = 1$

X-intercept: value of $x$ when $y = 0$

Substitute $0$ for $y$ and solve for $x$.

x-0=1

$x = 1$

The x-intercept is $\left(1 , 0\right)$. Plot this point.

Y-intercept: value of $y$ when $x = 0$

Substitute $0$ for $x$ and solve for $y$.

$0 - y = 1$

$- y = 1$

Multiply both sides by $- 1$. This will reverse the signs.

$- 1 \left(- y\right) = 1 \times - 1$

$y = - 1$

The y-intercept is $\left(0 , - 1\right)$. Plot this point.

Draw a straight line through the points.

graph{x-y=1 [-10, 10, -5, 5]}

Jul 29, 2018

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#### Explanation:

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We are given the equation: color(red)(x-y=1

How do we graph this linear equation ?

We have

color(blue)(x-y=1

The given equation can be reduced to a more simpler form.

Subtract color(red)(x from both sides of the equation:

$\Rightarrow x - y - x = 1 - x$

$\Rightarrow \cancel{x} - y - \cancel{x} = 1 - x$

$\Rightarrow - y = 1 - x$

Multiply both sides of the equation by color(red)((-1)

$\Rightarrow - y \cdot \left(- 1\right) = \left(1 - x\right) \left(- 1\right)$

$\Rightarrow y = x - 1$

Now, we have the equation in Slope-Intercept Form:

$\textcolor{b l u e}{y = m x + b}$, where

color(red)(m is the Slope and

color(red)(b is the y-intercept.

Hence,

Slope : color(blue)(1

y-intercept :color(blue)((0,-1)

The x-intercept is where the graph crosses the x-axis

Set color(red)(y=0 to find the x-intercept:

$\Rightarrow x - 1 = 0$

Add color(red)(1 to both sides of the equation:

$\Rightarrow x - 1 + 1 = 0 + 1$

$\Rightarrow x - \cancel{1} + \cancel{1} = 0 + 1$

$\Rightarrow x = 1$

Hence color(red)((1,0)# is the x-intercept.

Plot the points x-intercept and intercept on the graph.

Join the two points to get the straight line.

This is the graph of the linear equation.

Hope you find this solution useful.