Lesson 2-2 Linear Equations

Linear function – a function whose graph is a line. A linear function is represented by a linear equation. ex) y = 2x + 3 A solution of a linear equation is an ordered pair.

y = 3x + 2 Because the value of y depends on the value of x, y is called the DEPENDENT VARIABLE and x is called the INDEPENDENT VARIABLE

When graphing a linear equation make a t-chart. y = 3x + 2 To be sure you didn’t make a mistake graph at least three points.

y-intercept – point where the line crosses the y axis. What is the value of x at the y-intercept. x-intercept – point where the line crosses the x axis. What is the value of y at the x-intercept.

Slope Slope = vertical change = rise = y2 – y1 horizontal change run x2 – x1 Find the slope of the line that goes through the points ( -2, -2) and (4, 2)

Standard Form of a linear equation – is in the form Ax + By = C A must be positive. A, B, and C are integers. You can graph a linear equation in Standard Form by using the intercepts

When an equation is in standard form the slope = -A/B 2x + 3y = 7

Slope-intercept form y = mx + b slope y-intercept

Graph from Slope intercept form Put the y-intercept on the graph and use the slope to find other points

Write in standard form an equation of a line with slope 2 through (4, -2)

If you are given two points and asked to write an equation, Find the slope first, then write the equation. (5,0) (-3, 2)

Point-Slope Form The line through point (x1, y1) with slope m has the equation: y – y1 = m(x – x1)

Standard Form: Ax + By = C Point Slope Form: y – y1 = m(x – x1) Slope Intercept: y = mx + b

Horizontal lines m = 0 y is constant

Vertical Lines m is undefined x is constant

Parallel Lines m = m b1 = b2

Perpendicular Lines m2 is the opposite reciprocal of m1 m1 = -1/ m2

2-64 even pg 67 - 68