Full solution

Q. A line passes through the points

(-3, -4)

and

(6, -10)

. Write its equation in slope-intercept form.

Given points: Given points: $\newline$ $(-3, -4)$ and $\newline$ $(6, -10)$ $\newline$ Find the slope of the line using the points. $\newline$ Slope, $m$ $\newline$ $= \frac{y_2 - y_1}{x_2 - x_1}$ $\newline$ $= \frac{-10 - (-4)}{6 - (-3)}$ $\newline$ $= \frac{-10 + 4}{6 + 3}$ $\newline$ $= \frac{-6}{9}$ $\newline$ $= \frac{-2}{3}$ $\newline$ So, $m = -\frac{2}{3}$
Find slope: We have: $\newline$ $m: -\frac{2}{3}$ $\newline$ Choose one of the points to find the value of $b$ , the y-intercept. Let's use the point $(-3, -4)$ . $\newline$ Substitute $x = -3$ , $y = -4$ , and $m = -\frac{2}{3}$ in $y = mx + b$ . $\newline$ $-4 = \left(-\frac{2}{3}\right)(-3) + b$ $\newline$ $-4 = 2 + b$ $\newline$ $-4 - 2 = b$ $\newline$ $b$ $0$ $\newline$ So, $b$ $1$
Find y-intercept: We found: $\newline$ $m: -\frac{2}{3}$ $\newline$ $b: -6$ $\newline$ Write the equation of the line in slope-intercept form. $\newline$ Substitute $m = -\frac{2}{3}$ and $b = -6$ in $y = mx + b$ . $\newline$ $y = (-\frac{2}{3})x + (-6)$ $\newline$ $y = (-\frac{2}{3})x - 6$ $\newline$ Slope-intercept form: $y = (-\frac{2}{3})x - 6$