Question

write an equation in point - slope form for a line that passes through the given set of points. (-2, -4) and (1, 8)

Explanation:

Step1: Find the slope

The formula for slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let \( (x_1,y_1)=(-2,-4) \) and \( (x_2,y_2)=(1,8) \). Then \( m=\frac{8 - (-4)}{1 - (-2)}=\frac{8 + 4}{1+ 2}=\frac{12}{3}=4 \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). We can use either of the two points. Let's use the point \( (x_1,y_1)=(-2,-4) \) and \( m = 4 \). Substituting these values into the point - slope formula, we get \( y-(-4)=4(x - (-2)) \), which simplifies to \( y + 4=4(x + 2) \). We could also use the point \( (1,8) \), and the equation would be \( y - 8=4(x - 1) \).

Answer:

\( y + 4 = 4(x + 2) \) (or \( y - 8=4(x - 1) \))