Question

1. $y = -\frac{1}{2}x - 3$ $m = -\frac{1}{2}, b=(-3)$ (0,-3)

write an equation in slope - intercept form of two points.

1. (1,4) and (6,-1)

$x_1$ $y_1$ $x_2$ $y_2$
$m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-1 - 4}{6 - 1}=\frac{-5}{5}=-1$
$4=-1(1)+b$
$4=-1 + b$
$y=-1x + 5$

Explanation:

Step1: Calculate the slope $m$

The formula for slope between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Given $(x_1,y_1)=(1,4)$ and $(x_2,y_2)=(6, - 1)$, then $m=\frac{-1 - 4}{6 - 1}=\frac{-5}{5}=-1$.

Step2: Find the y - intercept $b$

Use the slope - intercept form $y=mx + b$ and substitute one of the points, say $(1,4)$ and $m=-1$ into it. So $4=-1\times1 + b$. Solving for $b$ gives $b=4 + 1=5$.

Step3: Write the equation

The slope - intercept form of the line is $y=mx + b$. Substituting $m=-1$ and $b = 5$ we get $y=-x + 5$.

Answer:

$y=-x + 5$