Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1

To graph linear equations. ALGEBRA 2 LESSON 2-2 Linear Equations 1-1

ALGEBRA 2 LESSON 2-2 Linear Equations 1-1 New Vocabulary Linear Function Linear Equation Dependant Variable Independent Variable Y-intercept X-Intercept Slope

Plot the points (0, 2) and (3, –2) and then draw the line through these two points. ALGEBRA 2 LESSON 2-2 Linear Equations Graph the equation y = – x If x = 0, then y = 2. If x = 3, then y = –2. 2-2

ALGEBRA 2 LESSON 2-2 Linear Equations Graph the equation 2-2

ALGEBRA 2 LESSON 2-2 Linear Equations Graph the equation 2-2

ALGEBRA 2 LESSON 2-2 Linear Equations The equation 10x + 5y = 40 models how you can give $.40 change if you have only dimes and nickels. The variable x is the number of dimes, and y is the number of nickels. Graph the equation. Describe the domain and the range. Explain what the x- and y-intercepts represent. 10x + 5y = 4010x + 5y = 40 10x + 5(0) = 4010(0) + 5y = 40 10x = 405y = 40 x = 4y = 8 Set x or y equal to zero to find each intercept. 2-2

The x-intercept is (4, 0), which means that the change can be given using 4 dimes and 0 nickels. The y-intercept is (0, 8), which means that the change can be given using 0 dimes and 8 nickels. ALGEBRA 2 LESSON 2-2 Linear Equations (continued) Use the intercepts to graph the equation. The number of dimes and the number of nickels must each be a whole number. The possible solutions for this situation are limited to those points on the line segment connecting (0, 8) and (4, 0) whose x- and y-coordinates are whole numbers. Therefore, the domain is {0, 1, 2, 3, 4} and the range is {0, 2, 4, 6, 8}. 2-2

ALGEBRA 2 LESSON 2-2 Linear Equations Find the slope of the line through the points (–2, 7) and (8, –6). Slope = Use the slope formula. y 2 –y 1 x 2 – x 1 = Substitute (–2, 7) for (x 1, y 1 ) and (8, –6) for (x 2, y 2 ). –6 – 7 8 – (–2) 2-2 = – Simplify The slope of the line is –

ALGEBRA 2 LESSON 2-2 Linear Equations Find the slope of the line through the points (–2, -2) and (4, 2). 2-2

ALGEBRA 2 LESSON 2-2 Linear Equations Find the slope of the line through the points (0, -3) and (-9, 6). 2-2

To write equations of lines. ALGEBRA 2 LESSON 2-2 Linear Equations 1-1

ALGEBRA 2 LESSON 2-2 Linear Equations 1-1 Standard Form of a Linear Equation

ALGEBRA 2 LESSON 2-2 Linear Equations 1-1 Point-Slope Form of a Linear Equation

ALGEBRA 2 LESSON 2-2 Linear Equations 1-1 Slope-Intercept Form of a Linear Equation

ALGEBRA 2 LESSON 2-2 Linear Equations Write in standard form an equation of the line with slope 3 through the point (–1, 5). y – y 1 = m(x – x 1 )Use the point-slope equation. y – 5 = 3[x – (–1)]Substitute 3 for m, 5 for y 1, and –1 for x 1. y – 5 = 3[(x + 1)]Simplify. y – 5 = 3x + 3Distributive Property 3x – y = –8Write in standard form. 2-2

ALGEBRA 2 LESSON 2-2 Linear Equations Write in standard form an equation of the line with slope 2 through the point (4, -2). 2-2

ALGEBRA 2 LESSON 2-2 Linear Equations Write in standard form an equation of the line with slope 5/6 through the point (5, 6). 2-2

ALGEBRA 2 LESSON 2-2 Linear Equations Write in point-slope form an equation of the line through (4, –3) and (5, –1). y – y 1 = m(x – x 1 )Write the point-slope equation. y + 3 = 2(x – 4)Simplify. You can also use (5, –1) for (x 1, y 1 ) and (4, –3) for (x 2, y 2 ). This gives the equation y + 1 = 2(x – 5). Both equations define the same line. y – y 1 = (x – x 1 )Substitute the slope formula for m. y 2 – y 1 x 2 – x 1 y – (–3) = (x – 4)Substitute: x 1 = 4, y 1 = –3, x 2 = 5, y 2 = –1. –1 – (–3) 5 – 4 2-2

ALGEBRA 2 LESSON 2-2 Linear Equations Write in point-slope form an equation of the line through (5, 0) and (-3, 2). 2-2

ALGEBRA 2 LESSON 2-2 Linear Equations Write in point-slope form an equation of the line through (-2, -1) and (-10, 17). 2-2

ALGEBRA 2 LESSON 2-2 Linear Equations Find the slope of –7x + 2y = 8. –7x + 2y = 8Add 7x to both sides. 2-2 y = x + 4Write in the slope-intercept form The slope of the line is. 7272

ALGEBRA 2 LESSON 2-2 Linear Equations Find the slope of 2-2

ALGEBRA 2 LESSON 2-2 Linear Equations Find the slope of 2-2

ALGEBRA 2 LESSON 2-2 Linear Equations Write an equation of the line in slope-intercept form through (5, –3) and perpendicular to y = 4x + 1. Graph both lines. 2-2 m = –Find the negative reciprocal of y = mx + bUse slope-intercept form. y = – x + bSlope is – –3 = – (5) + bSubstitute (5, –3) for (x, y). –3 = – + bSimplify – = bSolve for b y = – x – Write the equation

ALGEBRA 2 LESSON 2-2 Linear Equations Write an equation in slope-intercept form of the line through (-1, 3) and perpendicular to y = 5x-3. Graph both lines. 2-2

ALGEBRA 2 LESSON 2-2 Linear Equations Write an equation in slope-intercept form of the line through (0, 4) and perpendicular to y = 3/4x + 2. Graph both lines. 2-2

Algebra 2 Lesson 2-2 (Page 62) ALGEBRA 2 LESSON 2-2 Linear Equations 1-1