Question

question
what is an equation of the line that passes through the points (2, -3) and (1, 0)?

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \((x_1,y_1)=(2,-3)\) and \((x_2,y_2)=(1,0)\), so \( m=\frac{0 - (-3)}{1 - 2}=\frac{3}{-1}=-3 \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). We can use the point \((1,0)\) (we could also use \((2,-3)\)). Substituting \( m=-3 \), \( x_1 = 1 \) and \( y_1 = 0 \) into the point - slope form, we get \( y-0=-3(x - 1) \).

Step3: Simplify the equation

Simplify \( y-0=-3(x - 1) \) to get \( y=-3x + 3 \). We can also write it in standard form \( 3x+y=3 \), but the slope - intercept form \( y=-3x + 3 \) is a valid equation of the line.

Answer:

\( y=-3x + 3 \) (or \( 3x + y=3 \))