7 3 LINEAR EQUATIONS AND THEIR GRAPHS LINEAR

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7. 3 –LINEAR EQUATIONS AND THEIR GRAPHS

7. 3 –LINEAR EQUATIONS AND THEIR GRAPHS

LINEAR EQUATIONS

LINEAR EQUATIONS

EXAMPLE #1 GRAPH THE EQUATION 2 y – 4 = 4 x Solve for

EXAMPLE #1 GRAPH THE EQUATION 2 y – 4 = 4 x Solve for y and find three solutions. Y = 2 x + 2 x Y If x = 1, y = 2(1) + 2 = 4 1 4 If x = -2, y = 2(-2) + 2 = -2 -2 -2 3 8 If x = 3, y = 2(3) + 2 = 8

GRAPHING USING INTERCEPTS X – intercept – is the x-coordinate of the point where

GRAPHING USING INTERCEPTS X – intercept – is the x-coordinate of the point where the line intercepts the xaxis Y- intercept – is the y-coordinate of the point where the line intercepts the yaxis We can graph a linear equation by finding any two points that belong to the graph. Often the easiest points to find are the points where the graph crosses the axes. The graph shown on the right crosses the x- axis at (-2, 0) And the y-axis at (0, 3) We say that the x –intercept is -2 And the y-intercept is 3

EXAMPLE #2 GRAPH 4 x + 3 y = 12 USING INTERCEPTS To find

EXAMPLE #2 GRAPH 4 x + 3 y = 12 USING INTERCEPTS To find the x-intercept, let y = 0 and solve for x 4 x + 3(0) = 12 4 x = 12 x = 3 The x-intercept is 3 so we plot the point (3, 0) To find the y-intercept, let x = 0 and solve for y 4(0) + 3 y = 12 y = 4 The y-intercept is 4. We plot the point (0, 4) and draw the line

GRAPHING HORIZONTAL AND VERTICAL LINES The Standard Form of a linear equation in two

GRAPHING HORIZONTAL AND VERTICAL LINES The Standard Form of a linear equation in two variables is Ax + By = C, where A, B, and C are constants and A and B are not both 0 (zero).

EXAMPLE #3 Graph y = 3 Write the equation in standard form. (0)x +

EXAMPLE #3 Graph y = 3 Write the equation in standard form. (0)x + (1)y = 3 You can see that for any value of x, y =3. Thus, any ordered pair (x, 3), such as (0, 3), (4, 3), or (-1, 3), is a solution. The line is parallel to the x-axis with y-intercept 3.

EXAMPLE #4 Graph x = -4 Write this equation in standard form. (1)x +

EXAMPLE #4 Graph x = -4 Write this equation in standard form. (1)x + 0(y) = -4 You can see that for any value y. x = -4. Thus any ordered pair (-4, y), such as (-4, 3), (-4, 1), (-4, -1), Is a solution. The line is parallel to the y-axis with x-intercept -4.

HORIZONTAL AND VERTICAL LINES For constants a and b, - the graph of y

HORIZONTAL AND VERTICAL LINES For constants a and b, - the graph of y = b is the x-axis or a line parallel to the x-axis with y-intercept b. - the graph of x = a is the y-axis or a line parallel to y-axis with x-intercept a.

7. 4 - SLOPE

7. 4 - SLOPE

MEANING OF SLOPE r i s e run P (2, 1) Q (6, 3)

MEANING OF SLOPE r i s e run P (2, 1) Q (6, 3)

SLOPE DEFINITION

SLOPE DEFINITION

EXAMPLE #1 Graph the line containing points (-4, 2) and (2, -3) and find

EXAMPLE #1 Graph the line containing points (-4, 2) and (2, -3) and find the slope We plot the points and draw a line containing these points. We can use the definition of slope to find the slope of the line.

SLOPE

SLOPE

EXAMPLE #2

EXAMPLE #2

HORIZONTAL LINE

HORIZONTAL LINE

VERTICAL LINE

VERTICAL LINE

CONCLUSIONS FOR HORIZONTAL AND VERTICAL LINES A horizontal line has slope 0. A vertical

CONCLUSIONS FOR HORIZONTAL AND VERTICAL LINES A horizontal line has slope 0. A vertical line has no slope.

CLASSWORK (TO HAND IN – 10 POINT ASSIGNMENT) Graph these linear equations using three

CLASSWORK (TO HAND IN – 10 POINT ASSIGNMENT) Graph these linear equations using three points 1. 3 y – 12 = 9 x 2. 6 x – 27 = -2 Graphing using intercepts 3. 2 y = 3 x – 6 4. 5 x + 7 y = 35 Graph these equations 5. x = 5 6. y = -2