Warm Up If f(x)= 3x 2 + 2x, find f(3) and f(-2)

Check Yourself! If g(x)= 4x 2 – 8x + 2 find g(-3)

Goal Find the x intercept, y intercept and graph linear equations in various formats 3 forms Standard Form Ax + By = C Slope Intercept y = mx + b Point-Slope y 2 - y 1 = m(x 2 – x 1 )

Identifying a Linear Equation Ax + By = C y=mx + b (y 2 -y 1 )=m(x 2 -x 1 ) ● The exponent of each variable is 1. ● The variables are added or subtracted. ● A or B can equal zero. ● A > 0 ● Besides x and y, other commonly used variables are m and n, a and b, and r and s. ● There are no radicals in the equation. ● Every linear equation graphs as a line.

Examples of linear equations 2x + 4y =8 6y = 3 – x x = 1 -2a + b = 5 Equation is in Ax + By =C form Rewrite with both variables on left side … x + 6y =3 B =0 … x + 0 y =1 Multiply both sides of the equation by -1 … 2a – b = -5 Multiply both sides of the equation by 3 … 4x –y =-21

Examples of Nonlinear Equations 4x 2 + y = 5 xy + x = 5 s/r + r = 3 The exponent is 2 There is a radical in the equation Variables are multiplied Variables are divided The following equations are NOT in the standard form of Ax + By =C:

x and y -intercepts ● The x-intercept is the point where a line crosses the x-axis. The general form of the x-intercept is (x, 0). The y-coordinate will always be zero. ● The y-intercept is the point where a line crosses the y-axis. The general form of the y-intercept is (0, y). The x-coordinate will always be zero.

Finding the x-intercept ● For the equation 2x + y = 6, we know that y must equal 0. What must x equal? ● Substitute in 0 for y and simplify. 2x + 0 = 6 2x = 6 x = 3 ● So (3, 0) is the x-intercept of the line.

Finding the y-intercept ● For the equation 2x + y = 6, we know that x must equal 0. What must y equal? ● Substitute in 0 for x and simplify. 2(0) + y = y = 6 y = 6 ● So (0, 6) is the y-intercept of the line.

To summarize…. ●T●To find the x-intercept, plug in 0 for y. ●T●To find the y-intercept, plug in 0 for x.

Find the x and y- intercepts of x = 4y – 5 ● x-intercept: ● Plug in y = 0 x = 4y - 5 x = 4(0) - 5 x = x = -5 ● (-5, 0) is the x-intercept ● y-intercept: ● Plug in x = 0 x = 4y = 4y = 4y = y ● (0, ) is the y-intercept

Find the x and y-intercepts of 6x - 3y =-18 ● x-intercept ● Plug in y = 0 6x - 3y = -18 6x -3(0) = -18 6x - 0 = -18 6x = -18 x = -3 ● (-3, 0) is the x-intercept ● y-intercept ● Plug in x = 0 6x -3y = -18 6(0) -3y = y = y = -18 y = 6 ● (0, 6) is the y-intercept

Find the x and y-intercepts of x = 3 ● y-intercept ● A vertical line never crosses the y-axis. ● There is no y-intercept. ● x-intercept ● Plug in y = 0. There is no y. Why? ● x = 3 is a vertical line so x always equals 3. ● (3, 0) is the x-intercept. x y

Find the x and y-intercepts of y = -2 ● x-intercept ● Plug in y = 0. y cannot = 0 because y = -2. ● y = -2 is a horizontal line so it never crosses the x-axis. ● There is no x-intercept. ● y-intercept ● y = -2 is a horizontal line so y always equals -2. ● (0,-2) is the y-intercept. x y

Graphing Equations ● Example: Graph the equation -5x + y = 2 Solve for y first. -5x + y = 2Add 5x to both sides y = 5x + 2 ● The equation y = 5x + 2 is in slope-intercept form, y = mx+b. The y-intercept is 2 and the slope is 5. Graph the line on the coordinate plane.

x y Graph y = 5x + 2 Graphing Equations

Graph 4x - 3y = 12 ● Solve for y first 4x - 3y =12Subtract 4x from both sides -3y = -4x + 12 Divide by -3 y = x + Simplify y = x – 4 ● The equation y = x - 4 is in slope-intercept form, y=mx+b. The y -intercept is -4 and the slope is. Graph the line on the coordinate plane. Graphing Equations

Graph y = x - 4 x y Graphing Equations