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Download Logro 10. Graph Straight Lines.1
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Transcript
STRAIGHT-‐ LINE GRAPH Logro 10. Plots the graphs of linear functions in the form y = mx + c, finding the gradient. A graph is a set of infinite points that follows a rule. There are two main types of linear function. Horizontal and vertical lines Horizontal lines have equation y = a number. This example has several equations. http://www.mathcaptain.com/geometry/points-‐lines-‐and-‐planes.html Practice: What is the equation of these parallel lines? Vertical lines have equation x= a number http://www.mathcaptain.com/geometry/points-‐lines-‐and-‐planes.html Practice: What is the equation of these perpendicular lines? Diagonal lines As you go along a diagonal line, you move both across and up (or down). That means the equation of a diagonal line contains both an x and a y term. These diagonal lines always have equations y = mx + c. Later on we are going to see these further. http://math.tutorvista.com/geometry/straight-‐line.html Now, to graph linear equation there are available several strategies to do it. In this activity we are going to use two of them. Strategy 1 Steps to graph linear equations using tables 1. Solve the linear equation. This means, make y the subject. 2. Choose several values of x. Substitute each x-‐value in the equation and find the corresponding value of y. 3. Record the ordered-‐pair solution in a table 4. Graph the ordered-‐pair and draw a line through the points. Example 1. Make a solution table, and then graph the equation a) 8x + 4y = 12 b) -‐6x + 2y = 4 c) 9x -‐ 3y = 15 Follow the steps: a) 8x + 4y = 12 1. Make y the subject y = 2. Choose several values of x. Can we choose any values? Then which ones? 3. Make a Table x y 4. In your notebook, plot the points and connect them with a smooth curve. Note: Take into account the scale b) -‐6x + 2y = 4 1. Make y the subject y = 2. Choose several values of x. Can we choose any values? Then which ones? 3. Make a Table x y 4. In your notebook, plot the points and connect them with a smooth curve. Note: Take into account the scale c) 9x -‐ 3y = 15 1. Make y the subject y = 2. Choose several values of x. Can we choose any values? Then which ones? 3. Make a Table x y 4. In your notebook, plot the points and connect them with a smooth curve. Note: Take into account the scale Thinking Critically What is the fewest number of points needed to determine a line? Taken from Algebra 1 Strategy 2 Steps to graph linear equations using x-‐ and y-‐ intercepts Also the x-‐intercept and y-‐ intercept can be used to graph a linear equation. See these steps. 1. Write the equation in standard form: ax + by = c 2. Substitute 0 for y to find the x-‐intercept. 3. Substitute 0 for x to find the y-‐intercept. 4. Plot the intercepts and draw the graph. Example 2. Use the x-‐ and y-‐ intercepts to graph the equation a) x = 2y -‐3 b) 2x + y = 8 c) y = 4x -‐16 a) x = 2y -‐3 1. Write x = 2y -‐3 in standard form: ax + by = c 2. Find the x-‐intercept. So y = 0 (a, 0) 3. Find the y-‐intercept. So x = 0 (0, b) 4. Plot the intercepts and draw the graph. (Notebook) b) 2x + y = 8 1. Write 2x + y = 8 in standard form: ax + by = c 2. Find the x-‐intercept. So y = 0 (a, 0) 3. Find the y-‐intercept. So x = 0 (0, b) 4. Plot the intercepts and draw the graph. (Notebook) c) y = 4x -‐16 1. Write 2x + y = 8 in standard form: ax + by = c 2. Find the x-‐intercept. So y = 0 (a, 0) 3. Find the y-‐intercept. So x = 0 (0, b) 4. Plot the intercepts and draw the graph. (Notebook)
