LINEAR EQUATIONS PART I 1. Basic Coordinate Plane Info Assignments 2. Review on Plotting Points 3. Finding Slopes 4. x and y intercepts 5. Slope-Intercept Form of a Line 6. Graphing Lines7. Determine the equation of a line given two points, slope an
COORDINATE PLANE Y-axis Parts of a plane 1.X-axis 2.Y-axis QUAD II QUAD I 3.Origin 4.Quadrants I-IV Origin ( 0 , 0 ) X-axisQUAD III QUAD IV
PLOTTING POINTS Remember when plotting points you always start at B the origin. Next you go left C (if x-coordinate is negative) or right (if x-coordinate is positive. Then you go up (if y-coordinate is positive) or down (if y-coordinate is negative) AD Plot these 4 points A (3, -4), B (5, 6), C (-4, 5) and D (-7, -5)
SLOPESlope is the ratio of the vertical rise to the horizontalrun between any two points on a line. Usuallyreferred to as the rise over run.Run is 6 Slope triangle between two because we points. Notice that the slope went to the triangle can be drawn twoRise is 10 right different ways.because we Rise is -10went up because we went down −10 5 The slope in this case is = Run is -6 −6 3 because we went to the left 10 5 The slope in this case is = 6 3 Another way to find slope
FORMULA FOR FINDING SLOPE The formula is used when you know two points of a line.They look like A( X 1 , Y1 ) and B ( X 2 , Y2 ) RISE X 2 − X 1 X 1 − X 2SLOPE = = = RUN Y2 − Y1 Y1 − Y2 EXAMPLE
Find the slope of the line between the two points (-4, 8) and (10, -4) If it helps label the points. X 1 Y1 X2 Y2 Then use the formula X 2 − X1 (10) − (−4) Y2 − Y1 SUBSTITUTE INTO FORMULA (−4) − (8) (10) − (−4) 10 + 4 14 7 Then Simplify = = =− (−4) − (8) − 4 + (−8) − 12 6
X AND Y INTERCEPTSThe x-intercept is the x-coordinate of a pointwhere the graph crosses the x-axis.The y-intercept is the y-coordinate of a pointwhere the graph crosses the y-axis. The x-intercept would be 4 and is located at the point (4, 0). The y-intercept is 3 and is located at the point (0, 3).
SLOPE-INTERCEPT FORM OF A LINE The slope intercept form of a line is y = mx + b, where “m” represents the slope of the line and “b” represents the y-intercept. When an equation is in slope-intercept form the “y” is always on one side by itself. It can not be more than one y either. If a line is not in slope-intercept form, then we must solve for “y” to get it there. Examples
IN SLOPE-INTERCEPT NOT IN SLOPE-INTERCEPT y = 3x – 5 y – x = 10 y = -2x + 10 2y – 8 = 6x y = -.5x – 2 y + 4 = 2xPut y – x = 10 into slope-intercept form Add x to both sides and would get y = x + 10Put 2y – 8 = 6x into slope-intercept form. Add 8 to both sides then divide by 2 and would get y = 3x + 4Put y + 4 = 2x into slope-intercept form. Subtract 4 from both sides and would get y = 2x – 4.
GRAPHING LINES BY MAKING A TABLE OR USING THE SLOPE-INTERCEPT FORM I could refer to the table method by input-output table or x-y table. For now I want you to include three values in your table. A negative number, zero, and a positive number. Graph y = 3x + 2 INPUT (X) OUTPUT (Y) -2 -4 0 2 1 5By making a table it gives me three points, in this case (-2, -4) (0, 2) and (1, 5) to plotand draw the line. See the graph.
Plot (-2, -4), (0, 2) and (1, 5)Then draw the line. Make sure yourline covers the graph and hasarrows on both ends. Be sure touse a ruler. Slope-intercept graphing
Slope-intercept graphingSteps1.Make sure the equation is in slope-intercept form.2.Identify the slope and y-intercept.3.Plot the y-intercept.4.From the y-intercept use the slope to get another point to draw the line. 1. y = 3x + 2 2. Slope = 3 (note that this means the fraction or rise over run could be (3/1) or (-3/-1). The y-intercept is 2. 3. Plot (0, 2) 4. From the y-intercept, we are going rise 3 and run 1 since the slope was 3/1.
FIND EQUATION OF A LINE GIVEN 2 POINTS Find the equation of the line between (2, 5) and (-2, -3).1. Find the slope between the two points. 1. Slope is 2.2. Plug in the slope in the slope- 2. y = 2x + b intercept form. 3. Picked (2, 5) so3. Pick one of the given points and plug (5) = 2(2) + b in numbers for x and y. 4. b = 14. Solve and find b. 5. y = 2x + 15. Rewrite final form. Two other ways
Steps if given the slope and If given a graph there are three ways.a point on the line.1.Substitute the slope into One way is to find two points onthe slope-intercept form. the line and use the first method we talked about.2.Use the point to plug infor x and y. Another would be to find the3.Find b. slope and pick a point and use the second method.4.Rewrite equation. The third method would be to find the slope and y-intercept and plug it directly into y = mx + b.