SUMMARY
The discussion focuses on deriving the slope-intercept equation of a line parallel to the equation -9x - 7y = 4, while sharing the same y-intercept as -5x + 11y = -22. The slope of the first equation is determined to be -9/7, leading to the general form of the parallel line as y = (-9/7)x + c. The y-intercept of the second equation is calculated to be -2, resulting in the final equation of the parallel line as y = (-9/7)x - 2 or equivalently 9x + 7y = -14.
PREREQUISITES
- Slope-intercept form of a linear equation (y = mx + b)
- Understanding of parallel lines and their slopes
- Ability to manipulate linear equations
- Basic algebra skills for solving equations
NEXT STEPS
- Practice converting standard form equations to slope-intercept form
- Explore the properties of parallel and perpendicular lines in geometry
- Learn how to graph linear equations using slope and y-intercept
- Study systems of equations and their solutions
USEFUL FOR
Students learning algebra, educators teaching linear equations, and anyone seeking to understand the concepts of slope and y-intercept in mathematics.