Questions: Question 23, 3.4.3

Solution Steps

The line passes through the points (-8, -6) and (2, 4). To find the slope (m), use the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substitute the points: \[ m = \frac{4 - (-6)}{2 - (-8)} = \frac{4 + 6}{2 + 8} = \frac{10}{10} = 1 \]

The slope-intercept form of a line is \( y = mx + b \). We already have \( m = 1 \). To find \( b \), use one of the points, say (2, 4): \[ 4 = 1(2) + b \] \[ 4 = 2 + b \] \[ b = 2 \]

Now that we have the slope (m) and the y-intercept (b), we can write the equation of the line: \[ y = 1x + 2 \] \[ y = x + 2 \]

Final Answer