Question

what is an equation of the line that passes through the points (-1, -2) and (-2, -5)?

Explanation:

Step1: Calculate 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 \( (x_1,y_1)=(-1,-2) \) and \( (x_2,y_2)=(-2,-5) \). Then \( m=\frac{-5 - (-2)}{-2 - (-1)}=\frac{-5 + 2}{-2 + 1}=\frac{-3}{-1}=3 \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). We can use the point \( (-1,-2) \) and \( m = 3 \). Substitute into the formula: \( y-(-2)=3(x - (-1)) \), which simplifies to \( y + 2=3(x + 1) \).

Step3: Convert to slope - intercept form (optional)

Expand the right - hand side: \( y+2 = 3x+3 \). Subtract 2 from both sides: \( y=3x + 1 \). We can also write it in standard form \( 3x-y=-1 \), but the slope - intercept form \( y = 3x+1 \) is a valid equation of the line.

Answer:

The equation of the line is \( y = 3x+1 \) (or other equivalent forms like \( 3x - y=-1 \) or \( y+2 = 3(x + 1) \))