Question

the function that passes through the points (-2, 6) and (2, 7).

Explanation:

Step1: Find 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, \((x_1,y_1)=(-2,6)\) and \((x_2,y_2)=(2,7)\). So, \( m=\frac{7 - 6}{2-(-2)}=\frac{1}{4} \).

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 \((-2,6)\). Substitute \( m = \frac{1}{4} \), \( x_1=-2 \) and \( y_1 = 6 \) into the formula:
\( y-6=\frac{1}{4}(x + 2) \)

Step3: Simplify to slope - intercept form

Expand the right - hand side: \( y-6=\frac{1}{4}x+\frac{1}{2} \)
Add 6 to both sides. Since \( 6=\frac{12}{2} \), we have \( y=\frac{1}{4}x+\frac{1}{2}+\frac{12}{2}=\frac{1}{4}x+\frac{13}{2} \)

Answer:

The equation of the line is \( y=\frac{1}{4}x+\frac{13}{2} \) (or in standard form \( x - 4y=-26 \))