5Examples of linear equations Equation is in Ax + By =C formRewrite with both variables on left side …x + 6y =3B =0 … x + 0 y =1Multiply both sides of the equation by -1 … 2a – b = -5Multiply both sides of the equation by 3 … 4x –y =-212x + 4y =86y = 3 – xx = 1-2a + b = 5
6Examples of Nonlinear Equations The following equations are NOT in the standard form of Ax + By =C:The exponent is 2There is a radical in the equationVariables are multipliedVariables are divided4x2 + y = 5xy + x = 5s/r + r = 3
7Find the slope of a line through points (3, 4) and (-1, 6).
8Write an equation for the line that passes through (-2, 5) and (1, 7): Find the slope:Use point-slope form:
9Change into slope-intercept form and identify the slope and y-intercept.
11x-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.
12Horizontal 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 = -2Write an equation of a line and graph it that passes through (2, 4) and (-3, 4).y = 4
13Vertical 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 = 1Write an equation of a line that passes through (3, 5) and (3, -2).x = 3
14Graphing Lines graph a line. Using x and y intercepts: *You need at least 2 points tograph a line.Using x and y intercepts:Find the x and y interceptsPlot the pointsDraw your line
15Graph using x and y intercepts 2x – 3y = -12x-intercept2x = -12x = -6(-6, 0)y-intercept-3y = -12y = 4(0, 4)
16Graph using x and y intercepts 6x + 9y = 18x-intercept6x = 18x = 3(3, 0)y-intercept9y = 18y = 2(0, 2)
17Graphing 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 thecorresponding number of spaces up/down.Use the denominator of the slope to count the corresponding number of spaces left/right.Draw your line.
18Graph using slope-intercept form y = -4x + 1: y-intercept(0, 1)Slopem = -4 = -41
19Graph using slope-intercept form 3x - 4y = 8y = 3x - 24y-intercept(0, -2)Slopem = 34