Question

question
what is an equation of the line that passes through the points (-2, 3) and (-4, -2)?

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, \( (x_1, y_1)=(-2, 3) \) and \( (x_2, y_2)=(-4, -2) \). So, \( m=\frac{-2 - 3}{-4 - (-2)}=\frac{-5}{-2}=\frac{5}{2} \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Using the point \( (-2, 3) \) and \( m = \frac{5}{2} \), we have \( y - 3=\frac{5}{2}(x - (-2)) \), which simplifies to \( y - 3=\frac{5}{2}(x + 2) \).

Step3: Convert to slope - intercept form

Expand the right - hand side: \( y - 3=\frac{5}{2}x+5 \). Then add 3 to both sides: \( y=\frac{5}{2}x + 5+3 \), so \( y=\frac{5}{2}x+8 \). We can also convert it to standard form \( Ax+By = C \). Multiply through by 2 to get \( 2y = 5x+16 \), then rearrange to \( 5x-2y=-16 \).

Answer:

\( y=\frac{5}{2}x + 8 \) (or \( 5x-2y=-16 \) or other equivalent forms)