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Linear Equations and Inequalities5.1 Rectangular Coordinate System
Find the coordinates of each of the points Find the coordinates of each of the points Scatter Diagrams
5.2 Graphs of Straight Lines A solution of a linear equation in two variables is an ordered pair of numbers (x,y) that makes the equation a true statement. y = mx + b For y = 3x – 5, find the value of m and the value of b. Is (-1,-8) a solution? Is (2, -4) a solution of
Find the ordered pair solution of A graph of an equation in two variables is a drawing of
the ordered pair solutions of the equation. Graph y = 2x + 2 Graph y = -3x + 1 Graph
Graph
Graph y = 3x Graph equations of the form Write 5x – 2y = 10 in the form y = mx + b then graph the equation. Graph x – 3y = 9 x-intercept is where the graph crosses the x-axis, (x,0). Find the x- and y-intercepts for 4x – y = 4. Graph the line. Graph of y = b Graph of x = a Graph y = 3 Graph x = -4 5.3 Slopes of Straight Lines The slope of a line is the ratio of the change in the y-coordinates between any two points on the line to the change in x-coordinates. Slope = m = Find the slope of the line containing points (-1,1) and (2,3). Find the slope of the line containing points (-3,4) and (2,-2). Find the slope of the line containing points (-1,3) and (2,3). Find the slope of the line containing points (2,4) and (2,-2). Find the slope of the line containing points (-1,2) and (1,3). Find the slope of the line containing points (1,2) and (4,-5). Find the slope of the line containing points (2,3) and (2,7). Find the slope of the line containing points (1,-3) and (-5,-3). For any equation of the form Graph y = 2x + 3 Graph
Graph x – 2y = 4 5.4 Equations of Straight Lines Slope intercept form: y = mx + b Find the equation of the line that has slope 2 and y-intercept (0,3). Find the equation of the line that has slope 3/2 and contains the point (4,-2). Point-Slope Formula y – y1 = m(x – x1) Use the point slope formula to find the equation of a line that passed through the point whose coordinates are (-2, -1) and has slope 3/2. Use the point slope formula to find the equation of a line that passed through the point whose coordinates are (5,4) and has slope 2/5. 5.5 Functions Set = a collection of objects Eg. Relation = set of ordered pairs Eg. Domain of a relation = set of first coordinates of the ordered pairs. Eg. Range of a relation = set of second coordinates of the ordered pairs. Eg. Function = a relation where no two ordered pairs have the same first coordinate and different second coordinates. Eg. Find the domain and range of the relation {(-5, 1), (-3, 3), (-1, 5)}. Is the relation a function? Find the domain and range of the relation {(1,0), (1,1), (1,2), (1,4), (1,4)}. Is the relation a function? f(x) is the value of the function at x f(x) = x2 Evaluate f(x) = 2x – 4 at x = 3. Write an ordered pair that is an element of the function. Evaluate f(x) = -5x + 1 at x = 2. Write an ordered pair that is an element of the function. When a function is described by an equation and the domain is specified, the range of the function can be found. Find the range of the function given by the equation f(x) = -3x + 2 if the domain is {-4, -2, 0, 2, 4} Find the range of the function given by the equation f(x) = 4x - 3 if the domain is {-5, -3, -1, 1} Graphs of linear functions Equations of the form y = mx + b are functions. y = dependent variable Can write y = 2x + 1 in functional notation. Functions of the form f(x) = mx + b are called linear functions. Graph The value, V, of an investment of $2500 at an annual simple interest rate of 6% is given by the equation V = 150t + 2500, where t is the amount of time, in years, that the money is invested. Write the equation in functional notation. Graph the equation for values of t between 0 and 10. The point whose coordinates are (5,3250) is on the graph. Write a sentence that explains the meaning of this ordered pair. A car is traveling at a uniform speed of 40 mph. The distance, d (in miles), the car travels in t hours is given by the equation d = 40 t. Write the equation in functional notation. Graph the equation for values of t between 0 and 5. The point whose coordinates are (3, 120) is on the graph. Write a sentence that explains the meaning of this ordered pair. 5.6 Graphing Linear Inequalities. The graph of y = x + 1 separates a plane into three sets: y = x + 1 y > x + 1 y < x + 1 • Solve for y Graph the solution set of 2x + 3y ≤ 6. Graph the solution set of 3x + y > -2. Graph the solution set of y > 3. Graph the solution set of x < 3. |
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that corresponds to x = 4.
