# What is the slope, x-intercept, and y-intercept of the graph of 3x+y=7?

Mar 5, 2018

The slope m = -3
The y intercept = 7
The x intercept = $\frac{7}{3}$

#### Explanation:

The y intercept form is
$y = m x + b$

Changing the equation
$3 x + y = 7$ to get the y intercept form add $- 3 x$ to both sides

$3 x + \left(- 3 x\right) + y = - 3 x + 7$ which gives the y intercept form

$y = - 3 x + 7$

$m =$ the slope ( think mountain ski slope)$m = - 3$
$b =$ the y intercept ( thing beginning) $b = 7 \mathmr{and} \left(0 , 7\right)$

The x intercept form is

$x = m y + b$

Solve the equation for x

$3 x + y = 7 \text{ }$ subtract y from both sides

$3 x + y - y = - y + 7 \text{ }$ This gives

$3 x = - y + 7 \text{ }$ divide both sides by 3

$\frac{3 x}{3} = \frac{- y}{3} + \frac{7}{3}$ The result is

$x = - \frac{1}{3} \times y + \frac{7}{3}$

The $x$-intercept is $\frac{7}{3} \mathmr{and} \left(\frac{7}{3} , 0\right)$
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