Question

1. Write the equation of the line for the points (2,-1) and (-4,11).

Answer 1

Answer:

$y=-2x+3$

Step-by-step explanation:

Slope-intercept form of an equation is written as $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept.

The slope of a line that passes through the points $(x_1,\: y_1)$ and $(x_2, \: y_2)$ is $m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$. Using the coordinates $(2, -1)$ and $-4,11)$ as given in the problem, we have slope of this line to be:

$m=\frac{11-(-1)}{-4-2}=\frac{12}{-6}=-2$.

Now using this slope we've found and any point the line passes through, we can find the y-intercept of this equation:

$-1=-2(2)+b, \\ b=3$

Therefore, the equation of this line in slope-intercept form is $\fbox{ y=-2x+3 }$.