Question

1. what is the equation of the line that passes through the points (3,1) and (2,4)? (write your answer in slope - intercept form)

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(3,1)$ and $(x_2,y_2)=(2,4)$. Then $m=\frac{4 - 1}{2 - 3}=\frac{3}{-1}=- 3$.

Step2: Use point - slope form

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(3,1)$ and $m=-3$, we have $y - 1=-3(x - 3)$.

Step3: Convert to slope - intercept form

Expand the right side: $y - 1=-3x+9$. Add 1 to both sides to get $y=-3x + 10$.

Answer:

$y=-3x + 10$