Question: Determine the equation of the line that passes through the given points. (If you have a graphing calculator, you can use the table feature to confirm that the coordinates of both points satisfy your equation.)
$(3, 18)$ and $(8, 33)$
a.
$y = 3 x + 9$
b.
$y = \text{negative } 3 x \text{ minus } 9$
c.
$y = 3 x + 18$
d.
$y = \text{negative } 3 x + 9$
1. **State the problem:** Find the equation of the line passing through points $(3, 18)$ and $(8, 33)$.
2. **Formula for slope:** The slope $m$ of a line through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by
$$m = \frac{y_2 - y_1}{x_2 - x_1}$$
3. **Calculate the slope:**
$$m = \frac{33 - 18}{8 - 3} = \frac{15}{5} = 3$$
4. **Use point-slope form:**
The equation of the line is
$$y - y_1 = m(x - x_1)$$
Using point $(3, 18)$:
$$y - 18 = 3(x - 3)$$
5. **Simplify the equation:**
$$y - 18 = 3x - 9$$
Add $18$ to both sides:
$$y = 3x - 9 + 18$$
$$y = 3x + 9$$
6. **Check the options:** The correct equation is $y = 3x + 9$, which corresponds to option a.
**Final answer:** $y = 3x + 9$