Question

a. rewrite the equation 9x - 3y - 6 = 0 in slope-intercept form. b. give the slope and y-intercept. c. use the slope and y-intercept to graph the linear function. a. the slope-intercept form of the equation is (simplify your answer. use integers or fractions for any numbers in the equation.)

Explanation:

Step1: Isolate the y-term

$9x - 3y - 6 = 0 \implies -3y = -9x + 6$

Step2: Solve for y (divide by -3)

$y = \frac{-9x}{-3} + \frac{6}{-3} \implies y = 3x - 2$

Step3: Identify slope and intercept

Slope is the coefficient of $x$; y-intercept is the constant term.

Step4: Graphing instructions

1. Plot the y-intercept $(0, -2)$ on the coordinate plane.
2. Use the slope $3 = \frac{3}{1}$: from the y-intercept, move 3 units up and 1 unit right to plot a second point.
3. Draw a straight line through the two points.

Answer:

a. $y = 3x - 2$
b. Slope: $3$; y-intercept: $-2$ (or the point $(0, -2)$)
c. Graph: Plot $(0, -2)$, then use slope $\frac{3}{1}$ to plot a second point, then draw a line through the points.