Question

1. in standard form, write the equation of the line if $m = \frac{2}{3}$ and the y-intercept is 5.

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. Given $m=\frac{2}{3}$ and $b = 5$, we substitute these values into the slope - intercept form. So we get $y=\frac{2}{3}x+5$.

Step2: Convert to standard form

The standard form of a line is $Ax + By=C$, where $A$, $B$, and $C$ are integers and $A\geq0$. To convert $y=\frac{2}{3}x + 5$ to standard form, we first multiply every term by 3 to get rid of the fraction.
$3y=3\times(\frac{2}{3}x)+3\times5$
Simplifying, we have $3y = 2x+15$.
Then, we subtract $2x$ from both sides to get $- 2x+3y=15$. But we want $A\geq0$, so we multiply every term by $- 1$ to obtain $2x - 3y=-15$.

Answer:

The equation of the line in standard form is $2x - 3y=-15$