Question

write an equation of the line that passes through $(-1, 0)$ and $(0,0)$.
y = \square

Explanation:

Step1: Identify 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, \( (x_1, y_1)=(-1, 0) \) and \( (x_2, y_2)=(0, 0) \). So \( m=\frac{0 - 0}{0 - (-1)}=\frac{0}{1}=0 \).

Step2: Use slope - intercept form

The slope - intercept form of a line is \( y = mx + b \), where \( b \) is the y - intercept. The line passes through \( (0,0) \), so when \( x = 0 \), \( y = 0 \). Substituting \( m = 0 \) and \( (x,y)=(0,0) \) into \( y=mx + b \), we get \( 0=0\times0 + b \), so \( b = 0 \). Then the equation of the line is \( y=0x+0 \), which simplifies to \( y = 0 \).

Answer:

\( y = 0 \)