Question

a line passes through the points (-2, -4) and (4, 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, \( (x_1,y_1)=(-2,-4) \) and \( (x_2,y_2)=(4,6) \). So, \( m=\frac{6 - (-4)}{4 - (-2)}=\frac{6 + 4}{4 + 2}=\frac{10}{6}=\frac{5}{3} \).

Step2: Use point - slope form to find the equation

The point - slope form is \( y - y_1=m(x - x_1) \). Let's use the point \( (-2,-4) \). Substitute \( m = \frac{5}{3} \), \( x_1=-2 \) and \( y_1 = - 4 \) into the formula: \( y-(-4)=\frac{5}{3}(x - (-2)) \), which simplifies to \( y + 4=\frac{5}{3}(x + 2) \).

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

Expand the right - hand side: \( y+4=\frac{5}{3}x+\frac{10}{3} \). Then subtract 4 from both sides. Since \( 4=\frac{12}{3} \), we have \( y=\frac{5}{3}x+\frac{10}{3}-\frac{12}{3}=\frac{5}{3}x-\frac{2}{3} \).

Answer:

\( y=\frac{5}{3}x-\frac{2}{3} \)