Systems of Equations: Slopes and Intercepts

Systems of Equations: Slopes and y-intercepts

Comparing Slopes and y-intercepts

• Same Slope, Different y-intercepts: Parallel lines, no solution.
• Same Slope, Same y-intercept: Same line, infinitely many solutions.
• Different Slopes, Different y-intercepts: Intersecting lines, one solution.
• Different Slopes, Same y-intercept: Intersecting line, one solution.

Slope-intercept form

• The slope-intercept form of a linear equation is given by: y = mx + b, where m is the slope, and b is the y-intercept.

Slope Formula

• The formula to find the slope m between two points (x1, y1) and (x2, y2) is: m = \frac{y2 - y1}{x2 - x1}.

Determining the Number of Solutions

• No Solution: Lines have the same slope but different y-intercepts.
• One Solution: Lines have different slopes.
• Infinitely Many Solutions: Lines have the same slope and the same y-intercept.