Question

question 6 (1 point)
what is the slope-intercept form of $9x + 3y - 6 = 0$?
f. $y = 9x - 6$
g. $y = 3x + 2$
h. $y = 3x - 2$
j. $y = -3x + 2$
k. $y = -9x + 6$
options: a f, b g, c h, d j, e k

question 7 (1 point)
what is the slope of the line determined by the equation $2x - 3y = 6$?
f. $-6$
g. $-3$
h. $-\frac{3}{2}$
j. $\frac{2}{3}$
k. $2$
options: a f, b j, c h, d k, e g

Explanation:

Question 6 (Slope - Intercept Form)

Step 1: Recall the 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. We need to solve the equation $9x + 3y-6 = 0$ for $y$.
First, isolate the term with $y$:
Add $6 - 9x$ to both sides of the equation $9x+3y - 6=0$.
We get $3y=-9x + 6$.

Step 2: Solve for $y$

Divide each term in $3y=-9x + 6$ by 3.
$\frac{3y}{3}=\frac{-9x}{3}+\frac{6}{3}$
Simplifying, we have $y=-3x + 2$.

Step 1: Recall the slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope. We need to solve the equation $2x-3y = 6$ for $y$.
First, isolate the term with $y$:
Subtract $2x$ from both sides: $-3y=-2x + 6$.

Step 2: Solve for $y$

Divide each term in $-3y=-2x + 6$ by $-3$.
$\frac{-3y}{-3}=\frac{-2x}{-3}+\frac{6}{-3}$
Simplifying, we get $y=\frac{2}{3}x-2$.
The coefficient of $x$ is the slope, so the slope $m=\frac{2}{3}$.

Answer:

d. J. $y = - 3x+2$

Question 7 (Slope of the Line)