How do you graph the linear function $f (x) = \frac{2}{3} x + 1$ $f(x)=2/3x+1$ ?

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How do you graph the linear function $f (x) = \frac{2}{3} x + 1$ $f(x)=2/3x+1$ ?

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Answer 1 · 2017-05-09T18:07:10

$y = \frac{2}{3} x + 1$ $y=2/3x+1$

We need to know three things to graph a linear equation: $x$ $x$ -intercept, $y$ $y$ -intercept, and slope.

We can tell, thanks to $y = m x + b$ $y=color(red)(m)x+color(orange)(b)$ , that the $s l o p e$ $color(red)(slope)$ is $\frac{2}{3}$ $color(red)(2/3)$ and the $y - i n t e r c e p t$ $color(orange)(y-i n t ercept)$ is $1$ $color(orange)(1)$ . We have two out of the three required pieces of information, but we still need the $x -$ $x-$ intercept.

To find the $x$ $x$ -intercept, we need to set $y$ $y$ equal to zero and solve for $x$ $x$ :

$0 = \frac{2}{3} x + 1$ $0=2/3x+1$

subtract $1$ $1$ on both sides

$- 1 = \frac{2}{3} x$ $-1=2/3x$

multiply by $\frac{3}{2}$ $3/2$ on both sides

$3/2*-1/1=cancel(3)/cancel(2)*cancel(2)/cancel(3)x$

$-3/2=x$

So, the $x$ -intercept is $(-3/2,0)$ , the $y$ -intercept is $(0,1)$ , and the slope is $2/3$ . That means we begin at $(0,1)$ , and go up $2$ , over $3$ , and also down $2$ , over $3$ . We keep doing that forever (that's the nature of a line), and if everything is correct, the line should pass through the point $(-3/2,0)$ .

Let's check our work
graph{y=2/3x+1}

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How do you graph the linear function $f (x) = \frac{2}{3} x + 1$ $f(x)=2/3x+1$ ?

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