5­3 Slope­Intercept Form intercept (noun) IN tur sept Other Word Forms: intercepted (verb), interception (noun) Definition: An intercept is a point where someone or something is stopped along its way from one place to another. Main Idea: You can find the intercept(s) of a graph by finding the point(s) where the graph crosses a coordinate axis. Related Words: x­intercept; y­intercept A family of functions is a group of functions with common characteristics. A parent function is the simplest function with these characteristics. the linear parent function is y = x or f (x) = x . The graphs of three linear functions are shown below. A linear equation is an equation that models a linear function. In a linear equation, the variables cannot be raised to a power other than 1. So y = 2x is a linear equation, but y = x2 and y = 2x are not. The graph of a linear equation contains all the ordered pairs that are solutions of the equation. Graphs of linear functions may cross the y­axis at any point. A y­intercept of a graph is the y­coordinate of a point where the graph crosses the y­axis. Essential Understanding You can use the slope and y­intercept of a line to write and graph and equation of the line Find the slope and y­intercept of the graph of each equation. A.) y = 3x + 1
B.) y = 2x − 5
C.) y = 5x − 3
D.) y = 4
E.) y = 14 x − 13
Write an equation in slope­intercept form of the line with the given slope m and y­intercept b . F.) m = 3, b = 2
G.) m = 0.7, b =− 2
H.) m =− 2, b =
8
5
Write an equation in slope­intercept form of each line. I.) J.) K.) Write an equation in slope­intercept form of the line that passes through the given points. L.) (− 2, 4) and (3,− 1) Graph each equation. M.) y = x + 5
N.) y =− 2x + 1 Find the slope and the y­intercept of the graph of each equation. O.) y − 2 =− 3x
P.) y − 9x = 12 Q.) − 2y = 6 (5 − 3x)
R.) y = (2 − a) x + a Use the slope and y­intercept to graph each equation. S.) 2y + 4x = 0
T.) y + 2 = 5x − 4 U.) − 2 (3x + 4) + y = 0 Write a recursive formula and an explicit formula in slope­intercept form that model each arithmetic sequence. How does the recursive formula relate to the slope­intercept form? V.) ­1, 3, 7, 11, . . .