5 Examples 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
6 Examples 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
7 Find the slope of a line through points (3, 4) and (-1, 6).
8 Write an equation for the line that passes through (-2, 5) and (1, 7): Find the slope:Use point-slope form:
9 Change into slope-intercept form and identify the slope and y-intercept.
11 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.
12 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 = -2Write an equation of a line and graph it that passes through (2, 4) and (-3, 4).y = 4
13 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 = 1Write an equation of a line that passes through (3, 5) and (3, -2).x = 3
14 Graphing 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
15 Graph using x and y intercepts 2x – 3y = -12x-intercept2x = -12x = -6(-6, 0)y-intercept-3y = -12y = 4(0, 4)
16 Graph using x and y intercepts 6x + 9y = 18x-intercept6x = 18x = 3(3, 0)y-intercept9y = 18y = 2(0, 2)
17 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 thecorresponding number of spaces up/down.Use the denominator of the slope to count the corresponding number of spaces left/right.Draw your line.
18 Graph using slope-intercept form y = -4x + 1: y-intercept(0, 1)Slopem = -4 = -41
19 Graph using slope-intercept form 3x - 4y = 8y = 3x - 24y-intercept(0, -2)Slopem = 34