How do you graph $y - 2 = \frac{2}{3} (x - 4)$ $y-2=2/3(x-4)$ ?

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How do you graph $y - 2 = \frac{2}{3} (x - 4)$ $y-2=2/3(x-4)$ ?

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Answer 1 · 2017-06-28T15:01:37

See the explanation below.

Explanation:

Graph:

$y - 2 = \frac{2}{3} (x - 4)$ $y-2=2/3(x-4)$

The easiest way to find points on the line is to convert the given equation in point slope form to slope intercept form: $y = m x + b$ $y=mx+b$ , where $m$ $m$ is the slope, and $b$ $b$ is the y-intercept. In order to do this, solve the point slope equation for $y$ $y$ .

$y - 2 = \frac{2}{3} (x - 4)$ $y-2=2/3(x-4)$

Add $2$ $2$ to both sides.

$y = \frac{2}{3} (x - 4) + 2$ $y=2/3(x-4)+2$

Simplify $\frac{2}{3} (x - 4)$ $2/3(x-4)$ to $\frac{2 (x - 4)}{3}$ $(2(x-4))/3$ .

$y = \frac{2 (x - 4)}{3} + 2$ $y=(2(x-4))/3+2$

Expand.

$y = \frac{2 x}{3} - \frac{8}{3} + 2$ $y=(2x)/3-8/3+2$

Simplify.

$y = \frac{2}{3} x - \frac{8}{3} + 2$ $y=2/3x-8/3+2$

Multiply $2$ $2$ by $\frac{3}{3}$ $3/3$ to get the same denominator as $- \frac{8}{3}$ $-8/3$ .

$y = \frac{2}{3} x - \frac{8}{3} + 2 \times \frac{3}{3}$ $y=2/3x-8/3+2xx3/3$

Simplify.

$y = \frac{2}{3} x - \frac{8}{3} - \frac{6}{3}$ $y=2/3x-8/3-6/3$

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

Determine two or three points on the line by choosing values for $x$ $x$ and solving for $y$ $y$ .

$Points$ $"Points"$

$x = - 2,$ $x=-2,$ $y = - 2$ $y=-2$

$x = 0,$ $x=0,$ $y = - \frac{2}{3}$ $y=-2/3$

$x = 1,$ $x=1,$ $y = 0$ $y=0$

Plot the points and draw a straight line through them.

graph{y=2/3(x-4)+2 [-12.66, 12.65, -6.33, 6.33]}

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How do you graph $y - 2 = \frac{2}{3} (x - 4)$ $y-2=2/3(x-4)$ ?

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