Algebra I: Linear Equations: Challenge

# Hard Level Guide Stretch thinking with multi-step problems, application questions, and deeper reasoning. # Slope-Intercept Form A linear equation can be written y = mx + b, where m is the slope and b is the y-intercept. The slope measures steepness: rise over run. A positive slope rises left to right; a negative slope falls. A slope of zero is horizontal; undefined slope is vertical. # Graphing Linear Equations Plot the y-intercept first, then use the slope to find another point. Connect the points with a straight line. Alternatively, make a table of x and y values. The graph of a linear equation is always a line. # Point-Slope and Standard Form Point-slope form y − y₁ = m(x − x₁) builds a line from a point and slope. Standard form Ax + By = C is useful for systems and intercepts. Convert between forms by solving for y or distributing. # Applications and Systems Linear models describe constant rates of change: distance over time, cost per item, and salary plus commission. Systems of two linear equations can be solved by graphing, substitution, or elimination to find where lines intersect.