Question

Find the slope of the line between the points (-1, 3) and (5, 11).

Is the point (-4, -1) on the same line as the other two points? Use slope to justify your answer.

Answer 1

Explanation:

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)\\\\\left(x_1,\:y_1\right)=\left(-1,\:3\right),\:\\\left(x_2,\:y_2\right)=\left(5,\:11\right)\\\\m=(11-3)/(5-\left(-1\right))\\\\m =(11-3)/(5+1)\\\\m=(8)/(6)\\\\Simplify\\\\m=(11-3)/(5-\left(-1\right))`

Yes (-4, -1) is on the same line with the other wo points.

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)\\\\\\\mathrm{Slope\:}\left(-4,\:-1\right),\:\left(5,\:11\right)\\\left(x_1,\:y_1\right)=\left(-4,\:-1\right),\:\\\left(x_2,\:y_2\right)=\left(5,\:11\right)\\\\m=(11-\left(-1\right))/(5-\left(-4\right))\\\\Simplify\\m=(4)/(3)\\\\\mathrm{Slope\:}\left(-1,\:3\right),\:\left(-4,\:-1\right)\\\\\left(x_1,\:y_1\right)=\left(-1,\:3\right),\:\\\left(x_2,\:y_2\right)=\left(-4,\:-1\right)\\\\m=(-1-3)/(-4-\left(-1\right))\\\\Simplify\\\\m=(4)/(3)`