Questions: Find an equation of the line through the given pair of points. (-7,-8) and (-3,-6). The equation of the line is . Simplify your answer. Type an equation using x and y as the variables. Use integers or fractions for any numbers in the equation.

Solution Steps

To find the equation of the line passing through two given points, we can use the point-slope form of the equation of a line. The steps are as follows:

1. Calculate the slope (m) using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
2. Use the point-slope form \( y - y_1 = m(x - x_1) \) to write the equation.
3. Simplify the equation to the slope-intercept form \( y = mx + b \).

Given points \((-7, -8)\) and \((-3, -6)\), we calculate the slope \(m\) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the given points: \[ m = \frac{-6 - (-8)}{-3 - (-7)} = \frac{-6 + 8}{-3 + 7} = \frac{2}{4} = \frac{1}{2} \]

Using the point-slope form of the equation of a line: \[ y - y_1 = m(x - x_1) \] Substituting \(m = \frac{1}{2}\) and the point \((-7, -8)\): \[ y - (-8) = \frac{1}{2}(x - (-7)) \] \[ y + 8 = \frac{1}{2}(x + 7) \]

Simplify the equation to the slope-intercept form \(y = mx + b\): \[ y + 8 = \frac{1}{2}x + \frac{1}{2} \cdot 7 \] \[ y + 8 = \frac{1}{2}x + \frac{7}{2} \] Subtract 8 from both sides: \[ y = \frac{1}{2}x + \frac{7}{2} - 8 \] \[ y = \frac{1}{2}x + \frac{7}{2} - \frac{16}{2} \] \[ y = \frac{1}{2}x - \frac{9}{2} \]

Final Answer