Full solution

Q. Write the equation of the line that passes through the points

(-3,1)

and

(0,-3)

. Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

\newline

Answer:

Calculate Slope: Calculate the slope $m$ of the line using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ . Given points: $(-3,1)$ and $(0,-3)$ . Let's use $(x_1, y_1) = (-3, 1)$ and $(x_2, y_2) = (0, -3)$ . $m = \frac{-3 - 1}{0 - (-3)} = \frac{-4}{3} = -\frac{4}{3}$ .
Point-Slope Form: Use the point-slope form of the equation of a line: $y - y_1 = m(x - x_1)$ . $\newline$ We can use either of the two points for $(x_1, y_1)$ . Let's use the point $(-3, 1)$ . $\newline$ Point-slope form: $y - 1 = \left(-\frac{4}{3}\right)(x - (-3))$ .
Simplify Equation: Simplify the equation. $\newline$ $y - 1 = \left(-\frac{4}{3}\right)(x + 3)$ . $\newline$ Now distribute the slope $-\frac{4}{3}$ across $(x + 3)$ . $\newline$ $y - 1 = \left(-\frac{4}{3}\right)x - \left(\frac{4}{3}\right)\cdot 3$ . $\newline$ $y - 1 = \left(-\frac{4}{3}\right)x - 4$ .
Check Equation: Check if the equation is fully simplified and in the correct form. $\newline$ The equation $y - 1 = \left(-\frac{4}{3}\right)x - 4$ is in point-slope form and is fully simplified.