# How do you find the slope and y intercept for y + 4 = 2x?

Mar 11, 2016

$m = 2$

$q = - 4$

#### Explanation:

We need to transform the equation in the form:

$y = m x + q$

where

slope=$m$

and

${y}_{\cap} = q$ (with ${y}_{\cap}$ as $y$ intercept)

$y + 4 = 2 x \iff y = 2 x - 4$

Therefore:

$m = 2$

$q = - 4$

graph{2x-4 [-3.862, 6.004, -4.428, 0.506]}

Mar 11, 2016

Same thing just, presented a bit differently!

$\textcolor{b l u e}{\text{The slope " = " } 2}$
color(blue)(" " y_("intercept ")=-4)

#### Explanation:

Given:$\text{ } y + 4 = 2 x$

You could transform this into the standard format of $y = m x + c$ but in this case we do not have to do so to determine what we are asked to.

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The y-intercept is when $x = 0$ This is because the y-axis crosses the x-axis at $x = 0$

So we write the equation as: $y + 4 = 2 \times 0$

But $2 \times 0 = 0$ giving

$\textcolor{b r o w n}{y + 4 = 0}$

Subtract$\text{ "color(blue)( 4 )" }$from both sides

$\textcolor{b r o w n}{y + 4 \textcolor{b l u e}{- 4} = \textcolor{b l u e}{- 4}}$

But $4 - 4 = 0$ giving

color(green)(y+0=-4" so " y_("intercept")=-4)
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The slope (gradient) is the number in front of x" ( the coefficient of "x)  which is 2

$\textcolor{g r e e n}{\text{The slope } = 2}$
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