Algebra 1 Chapter 3 Mid Chapter Review

Linear Equations

• Equation form: Ax + By = C; confirms the representation of linear equations.
• Example conversion: y = 2x - 1 is a linear equation; standard form representation is 2x - y = 1.

y-Intercept

• Determining the y-intercept from the equation 3x - 2y = -6 leads to finding the point (0, 3).

Distance and Rate

• A car traveling at 58 miles per hour for 7 hours can be estimated to cover 406 miles, derived from the equation d = 58t.

Intercepts

• For the equation 3x - y = 3, the x-intercept is (15, 0) and the y-intercept is (0, -3).

Solving Equations

• Finding the zero of the equation 3x - 45 = 0 results in the root being (15, 0).

Slope Calculation

• The slope between points (5, 8) and (-4, 6) is computed to be 2/9.
• For points (9, 4) and (5, -3), the slope is calculated as 7/4.

Unknown Variable

• Given points (3, 2) and (r, -4) with a slope of 3/2, the value of r is determined to be -1.

Linear Function Test

• A given set of points shows a non-linear relationship, as plotted coordinates (0, 1), (-2, -1), and (-4, 1) do not form a straight line.

Rate of Change

• From 2004 to 2010, the Delaware High School band increased from 275 to 305 students, calculating as an increase of 5 students per year.