Question

1. without graphing, what is the equation of the line that passes through the points (- 4, 3) and (6, -2)?

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, \((x_1,y_1)=(-4,3)\) and \((x_2,y_2)=(6, - 2)\). So, \( m=\frac{-2 - 3}{6-(-4)}=\frac{-5}{10}=-\frac{1}{2} \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Let's use the point \((-4,3)\) and \( m =-\frac{1}{2} \). Substitute into the formula: \( y - 3=-\frac{1}{2}(x + 4) \).

Step3: Simplify to slope - intercept form

Expand the right - hand side: \( y-3=-\frac{1}{2}x-2 \). Then, add 3 to both sides: \( y=-\frac{1}{2}x + 1 \). We can also write it in standard form \( x + 2y=2 \), but the slope - intercept form is also correct.

Answer:

The equation of the line is \( y=-\frac{1}{2}x + 1 \) (or in standard form \( x + 2y=2 \))