Algebra 1 - Chapter 5 Quiz Review

Slope Concepts

• Slope formula is calculated as ( \frac{y_2 - y_1}{x_2 - x_1} ).
• Point-slope form is expressed as ( y - y_1 = m(x - x_1) ).
• Slope-intercept form is given as ( y = mx + b ).

Direct Variation

• Direct Variation formula is ( y = kx ), where ( k ) represents the constant of variation.
• Every Direct Variation graph passes through the origin (0,0).

Point-Slope Form Equations

• Example equation through point (5, 1) with slope ( \frac{1}{3} ) is ( y - 1 = \frac{1}{3}(x - 5) ).
• Example equation through point (-2, 3) with slope -2 is ( y - 3 = -2(x + 2) ).

Standard Form Applications

• Standard form assists in determining the x and y intercepts of a line.

Graphing Examples

• Graphing the equation ( y = 4x - 4 ).
• Graphing the equation ( y = -x - 2 ).

Direct Variation Verification

• The equation ( 2x + 3y = 0 ) represents Direct Variation.
• The equation ( 4x + 6y = 3 ) does not represent Direct Variation.

Slope Calculations

• The slope between points (1, 1) and (10, 5) is ( \frac{4}{9} ).
• The slope between points (5, 9) and (2, 4) is ( \frac{5}{3} ).

Slope Characteristics

• Positive slope indicates a line that rises from left to right.
• Negative slope indicates a line that falls from left to right.
• Zero slope indicates a horizontal line with no vertical change.
• Undefined slope indicates a vertical line with no horizontal change.