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2.3 Linear Functions and Slope-Intercept Form Learning Target: I can Graph linear equations I can write equations of lines.

Review of Formulas Formula for Slope Point-Slope Form Slope-intercept Form Standard Form *where A>0 and A, B, C are integers

Review Slope

Examples of linear equations 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 2x + 4y =8 6y = 3 – x x = 1 -2a + b = 5

Examples of Nonlinear Equations The following equations are NOT in the standard form of Ax + By =C: The exponent is 2 There is a radical in the equation Variables are multiplied Variables are divided 4x2 + y = 5 xy + x = 5 s/r + r = 3

Find the slope of a line through points (3, 4) and (-1, 6).

Write an equation for the line that passes through (-2, 5) and (1, 7): Find the slope: Use point-slope form:

Change into slope-intercept form and identify the slope and y-intercept.

Change into standard form.

x-intercepts and y-intercepts The intercept is the point(s) where the graph crosses the axis. To find an intercept, set the other variable equal to zero.

Horizontal Lines Slope is zero. Equation form is y = #. Write an equation of a line and graph it with zero slope and y-intercept of -2. y = -2 Write an equation of a line and graph it that passes through (2, 4) and (-3, 4). y = 4

Vertical Lines Slope is undefined. Equation form is x = #. Write an equation of a line and graph it with undefined slope and passes through (1, 0). x = 1 Write an equation of a line that passes through (3, 5) and (3, -2). x = 3

Graphing Lines graph a line. Using x and y intercepts: *You need at least 2 points to graph a line. Using x and y intercepts: Find the x and y intercepts Plot the points Draw your line

Graph using x and y intercepts 2x – 3y = -12 x-intercept 2x = -12 x = -6 (-6, 0) y-intercept -3y = -12 y = 4 (0, 4)

Graph using x and y intercepts 6x + 9y = 18 x-intercept 6x = 18 x = 3 (3, 0) y-intercept 9y = 18 y = 2 (0, 2)

Graphing Lines Using slope-intercept form y = mx + b: Change the equation to y = mx + b. Plot the y-intercept. Use the numerator of the slope to count the corresponding number of spaces up/down. Use the denominator of the slope to count the corresponding number of spaces left/right. Draw your line.

Graph using slope-intercept form y = -4x + 1: y-intercept (0, 1) Slope m = -4 = -4 1

Graph using slope-intercept form 3x - 4y = 8 y = 3x - 2 4 y-intercept (0, -2) Slope m = 3 4

Homework Homework: p. 78 #7, 11, 17, 19, 23, 25, 27, 29, 31, 33, 37, 39, 43, 49, 53 Challenge - # 62