poprskanvxcl

2023-02-27

How to find a standard form equation for the line with slope 2/3 that passes through the point (3,6)?

koddann2hm9

The statement gives that $m=\frac{2}{3}$, so we have to find the value of $b$
Now, we also know that the line passes through $\left(3,6\right)$, and so:
$6=\frac{2}{3}\cdot 3+b$ and then $6=2+b$ and so $b=4$. The equation of the line is then:
$y=\frac{2}{3}x+4$

Idabuluq3xg

Finding the equation's slope-intercept form first, then changing it to standard form, is the first step.
The slope-intercept form is
$y=mx+b$
The slope $m$ is given as $\frac{2}{3}$, so the equation up to that point is $y=\frac{2}{3}x+b$
Substitute the values for $x$ and $y$ from the ordered pair provided in the problem to determine $b$
$6=\frac{2}{3}\left(\frac{3}{1}\right)+b$
Solve for $b$
1) Clear the parentheses by multiplying the fractions
$6=2+b$
2) Subtract $2$ from both sides to isolate $b$
$4=b$
So the slope-intercept form of the equation is
$y=\left(\frac{2}{3}\right)x+4$ $←$ slope-intercept form
The slope-intercept form should be changed to standard form.
Standard form is
$ax+by=c$ where $a$ is a positive whole digit
1) Clear the fraction by multiplying all the terms on both sides by $3$ and letting the denominator cancel
$3y=2x+12$
2) Subtract $2x$ from both sides to get the $x$ and $y$ terms on the same side
$-2x+3y=12$
3) Multiply through by $-1$ to clear the minus sign
$2x-3y=-12$ $←$ standard form

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