Question

Write the slope intercept of the equation of the line through the given points. Through (-2,-4) and (-3,-5)

Answer 1

The slope between two(2) points;

$\begin{gathered} P(x_1,y_1)_{} \\ \text{and Q(x}_2,y_2) \end{gathered}$

is given as:

$m=\frac{y_2-y_1}{x_2-x_1}$

From the question, the given points are:

$\begin{gathered} (-2,-4)\text{ and (-3,-5)} \\ \Rightarrow x_1=-2,y_1=-4 \\ \Rightarrow x_2=-3,y_2=-5 \end{gathered}$

Thus, the slope, m, is:

$\begin{gathered} m=\frac{-5-(-4)}{-3-(-2)} \\ m=\frac{-5+4}{-3+2} \\ m=\frac{-1}{-1} \\ m=-1 \end{gathered}$

The equation of a line with two(2) given points is given as:

$m=\frac{y-y_1}{x-x_1}$

Thus,

$\begin{gathered} -1=\frac{y-(-4)}{x-(-2)} \\ -1=\frac{y+4}{x+2} \\ \text{cross}-\text{multiply} \\ y+4=-1(x+2) \\ y+4=-x-2 \\ y=-x-2-4 \\ y=-x-6 \end{gathered}$

Hence, the slope-intercept form of the equation of the line through the given points is:

$y=-x-6$