Question

horizontal lines
what is the equation of the line that passes through the points (-4, -4) and (6, -4)?

1. find the slope of the line. m =
2. find the y - intercept of the line. b =
3. write the equation of the line in slope - intercept form.

Explanation:

Step 1: Find the slope of the line

The slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Let \((x_1, y_1) = (-4, -4)\) and \((x_2, y_2) = (6, -4)\).
Substitute into the formula: \( m = \frac{-4 - (-4)}{6 - (-4)} = \frac{-4 + 4}{6 + 4} = \frac{0}{10} = 0 \).

Step 2: Find the y - intercept of the line

The slope - intercept form of a line is \( y = mx + b \). We know \( m = 0 \) and we can use one of the points, say \((-4, -4)\), to find \( b \).
Substitute \( x=-4\), \( y = - 4\) and \( m = 0\) into \( y=mx + b \):
\(-4=0\times(-4)+b\)
Simplify the right - hand side: \(-4 = 0 + b\), so \( b=-4 \).

Step 3: Write the equation of the line in slope - intercept form

The slope - intercept form is \( y=mx + b \). We know that \( m = 0 \) and \( b=-4 \).
Substitute these values into the formula: \( y=0\times x-4\), which simplifies to \( y=-4 \).

Answer:

s:

1. The slope \( m=\boldsymbol{0} \)
2. The y - intercept \( b=\boldsymbol{-4} \)
3. The equation of the line is \( \boldsymbol{y=-4} \)