Question

8)
equation ______________
ordered pair = __(3,-3)
slope (m) = _______
y-intercept = 1

Explanation:

Step1: Recall the slope-intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know that $b = 1$ (given y - intercept) and we have an ordered pair $(x,y)=(3, - 3)$.

Step2: Substitute into the equation to find m

Substitute $x = 3$, $y=-3$ and $b = 1$ into $y=mx + b$:
$$-3=m\times3 + 1$$
Subtract 1 from both sides:
$$-3-1=3m$$
$$-4 = 3m$$
Divide both sides by 3:
$$m=-\frac{4}{3}$$

Step3: Write the equation

Now that we have $m =-\frac{4}{3}$ and $b = 1$, the equation of the line in slope - intercept form is $y=-\frac{4}{3}x + 1$

Answer:

• slope (m) : $-\frac{4}{3}$
• equation: $y =-\frac{4}{3}x + 1$