# How do you find the slope and intercept of y = - x + 2?

Apr 24, 2016

Slope is $- 1$, $y$ intercept is $2$.

#### Explanation:

The equation of the graph is given in the form

$y = m x + b = - x + 2$

where $m$ is the gradient or slope, and $b$ is the intercept on the $y$ axis.

By simply comparing the two equations, we can see that $m = - 1$ and $b = 2$.

This means the graph has a slope of $- 1$, and crosses the $y$ axis at point $\left(0 , 2\right)$.

Apr 24, 2016

y-intercept$\to \left(x , y\right) = \left(0 , 2\right)$
x-intercept->(x,y)=(2,0

#### Explanation:

Compare to $y = m x + c$

$m \to \text{gradient (slope)}$
$c \to \text{y-intercept}$

Given:$\text{ } y = - x + 2$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Determine gradient}}$

Write as:$\text{ } y = \left[\left(- 1\right) \times x\right] + 2$

color(blue)("The gradient "->m=-1
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Determine y-intercept}}$

color(blue)("y-intercept"->c=2

$\textcolor{b r o w n}{\text{To prove y-intercept = 2}}$

The graph crosses the y-axis at x=0. Substituting this value:

color(brown)(y=-x+2" "->" "color(blue)(y=-(0)+2 = 2

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Determine x-intercept}}$

The graph crosses the x-axis at y=0. Substituting this value

$\text{ } 0 = - x + 2$

Add $x$ to both sides

$\text{ } 0 + x = - x + x + 2$

color(blue)(" "x=0+2
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~