IVP combines differential equation with a starting point (initial value). Written as y' = f(x,y) with y(a) = b. Solution found by plugging initial value into general solution
X and y graph consists of horizontal (x-axis) and vertical (y-axis) axes. Origin is where axes intersect and serves as reference point. Points are represented by ordered pairs (x,y). Graph has four quadrants, each perpendicular line represents one quadrant
Slope intercept form is used to find equation of a straight line. Formula: y = mx + b, where m is slope and b is y-intercept. Equation must satisfy coordinates of points on line
Coefficient is a multiplicative factor in polynomial or series expressions. Can be numerical factor (number without units) or constant multiplier. May include variables like a, b, c. When variables and constants aren't products, called parameter
A linear system consists of two or more equations involving the same variables. A solution is an assignment of values that satisfies all equations simultaneously. Linear systems are fundamental in modern mathematics and engineering
Linear equations use y=mx+b formula with slope (m) and y-intercept (b). Y-intercept is always plotted at x=0. Slope is calculated as rise over run, plotted from y-intercept. Graph should be drawn using Cartesian coordinate plane