Question

a line passes through the points (-4, -4) and (1, 6). write its equation in slope-intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

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

Step2: Use point - slope form to find the equation

The point - slope form is \( y - y_1=m(x - x_1) \). Using the point \( (-4,-4) \) and \( m = 2 \), we have \( y-(-4)=2(x-(-4)) \), which simplifies to \( y + 4=2(x + 4) \).

Step3: Convert to slope - intercept form (\( y=mx + b \))

Expand the right - hand side: \( y+4=2x+8 \). Subtract 4 from both sides: \( y=2x+8 - 4=2x + 4 \).

Answer:

\( y = 2x+4 \)