Answer:
[tex]y=3x+9[/tex]
Step-by-step explanation:
We want to determine the equation of the line that passes through the points (3, 18) and (8, 33).
First, let’s determine the slope. We can use the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We will let (3, 18) be (x₁, y₁) and (8, 33) be (x₂, y₂). Then it follows that:
[tex]\begin{aligned} m&=\frac{33-18}{8-3} \\ m&=\frac{15}{3} \\ m&=3\end{aligned}[/tex]
Hence, the slope is 3.
Now, we can use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
We will substitute 3. for m. We can use either of the two points for (x₁, y₁) but let’s let (3, 18) be (x₁, y₁) for consistency. Thus:
[tex]y-18=3(x-3)[/tex]
Then it follows that:
[tex]\begin{aligned} y-18&=3x-9 \\ y&=3x+9 \end{aligned}[/tex]
Therefore, our equation is:
[tex]y=3x+9[/tex]
