Question

what is the equation in slope-intercept form of the line that passes through the points (-4, 2) and (12, 6)?
a ( y = 0.25x + 3 )
b ( y = 0.25x - 4.5 )
c ( y = 4x + 18 )
d ( y = 4x - 42 )

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, \((x_1, y_1)=(-4, 2)\) and \((x_2, y_2)=(12, 6)\). So, \( m=\frac{6 - 2}{12-(-4)}=\frac{4}{16}=0.25 \).

Step2: Use point - slope form to find the equation

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Using the point \((-4, 2)\) and \( m = 0.25 \), we have \( y - 2=0.25(x+4) \).

Step3: Simplify to slope - intercept form

Expand the right - hand side: \( y - 2=0.25x + 1 \). Then, add 2 to both sides: \( y=0.25x+1 + 2=0.25x + 3 \).

Answer:

A. \( y = 0.25x+3 \)