Question

use the given conditions to write an equation for the line in point - slope form and slope - intercept form. passing through (-4, -4) and (4, 8) type the point - slope form of the equation of the line. (use integers or simplified fractions for any numbers in the equation.) type the slope - intercept form of the equation of the line. (use integers or simplified fractions for any numbers in the equation.)

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, \((x_1, y_1)=(-4,-4)\) and \((x_2, y_2)=(4,8)\). So, \( m=\frac{8 - (-4)}{4 - (-4)}=\frac{12}{8}=\frac{3}{2} \).

Step2: Point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Using the point \((-4,-4)\) and \( m = \frac{3}{2} \), we get \( y-(-4)=\frac{3}{2}(x - (-4)) \), which simplifies to \( y + 4=\frac{3}{2}(x + 4) \).

Step3: Slope - intercept form

Start with the point - slope form \( y + 4=\frac{3}{2}(x + 4) \). Distribute the \(\frac{3}{2}\): \( y+4=\frac{3}{2}x+6 \). Subtract 4 from both sides: \( y=\frac{3}{2}x+6 - 4=\frac{3}{2}x + 2 \).

Answer:

Point - slope form: \( y + 4=\frac{3}{2}(x + 4) \)
Slope - intercept form: \( y=\frac{3}{2}x + 2 \)