Questions: The equation for line j can be written as y=-5/7 x-10. Line k, which is parallel to line j, includes the point (-9,5). What is the equation of line k? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Solution Steps

To find the equation of a line parallel to a given line, we need to use the same slope as the given line. The given line's equation is \( y = -\frac{5}{7}x - 10 \), so the slope is \( -\frac{5}{7} \). We then use the point-slope form of the equation of a line, \( y - y_1 = m(x - x_1) \), where \( m \) is the slope and \( (x_1, y_1) \) is the given point. Finally, we convert the equation to slope-intercept form, \( y = mx + b \).

The slope of the given line \( j \) is \( m = -\frac{5}{7} \). Since line \( k \) is parallel to line \( j \), it will have the same slope.

Using the point-slope form of the equation of a line, we have: \[ y - y_1 = m(x - x_1) \] Substituting \( m = -\frac{5}{7} \) and the point \( (-9, 5) \): \[ y - 5 = -\frac{5}{7}(x + 9) \]

Expanding and rearranging the equation: \[ y - 5 = -\frac{5}{7}x - \frac{45}{7} \] Adding 5 (which is \( \frac{35}{7} \)) to both sides: \[ y = -\frac{5}{7}x - \frac{45}{7} + \frac{35}{7} \] This simplifies to: \[ y = -\frac{5}{7}x - \frac{10}{7} \]

Final Answer