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

Beginner2023-02-28Added 5 answers

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 $(3,6)$, 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:

$y=\frac{2}{3}x+4$

Now, we also know that the line passes through $(3,6)$, 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

Beginner2023-03-01Added 6 answers

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

$y=\left(\frac{2}{3}\right)x+4$ $\leftarrow$ 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

$2x-3y=-12$ $\leftarrow$ standard form

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

$y=\left(\frac{2}{3}\right)x+4$ $\leftarrow$ 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

$2x-3y=-12$ $\leftarrow$ standard form