1.2 Slopes and Intercepts equation for a given line in the coordinate Objectives: Graph a linear equation. Write a linear equation for a given line in the coordinate plane. Standards: 2.8.11.K Apply an appropriate technique to graph a linear function. 2.8.11.L Write the equation of a line when given the graph of the line.

Y = 3x - 2 m = 3, b = -2 Y = 1/2x + 3/4 m = ½, b = ¾ m = 0, b = 5 I. Write the equation in slope-intercept form for the line that has the indicated slope, m, and y-intercept, b. m = 3, b = -2 Y = 3x - 2 Y = 1/2x + 3/4 m = ½, b = ¾ Y = 5 m = 0, b = 5 Y = -2x m = -2, b = 0

II. Identify the slope, m, and y-intercept, b, for each line II. Identify the slope, m, and y-intercept, b, for each line. Then graph. Positive slope goes up to the right & negative slope goes up to the left. x + y = 6 * m = _______ b = _______ y = x + 3 * m = _______ b = _______

II. Identify the slope, m, and y-intercept, b, for each line II. Identify the slope, m, and y-intercept, b, for each line. Then graph. 3x + 6y = 18 * m = ________ b = ________

III. Find the slope of a line if you know the coordinates of two points on the line. In a graph, the slope of a line is the change in vertical units divided by the corresponding change in the horizontal units. M = Change in Y = Rise = Y2 – Y1 Change in X Run X2 – X1 (0, 4) and (3, 1)

M = Change in Y = Rise = Y2 – Y1 Change in X Run X2 – X1 * (1, -3) and (3, -5) (3, -2) and (4, 5) (-10, -4) and (-3, -3)

IV. Find the x and y intercepts. The x intercept of a graph is the x-coordinate of the point where the graph crosses the x-axis. In order to find the x intercept (x, 0), substitute zero for y in an equation for the line and solve for x. The y intercept of a graph is the y-coordinate of the point where the graph crosses the y-axis. In order to find the y intercept (0, y), substitute zero for x in an equation for the line and solve for y.

IV. Find the x and y intercepts. 4x + y = -4 X Intercept 4x + 0 = -4 4x = -4 x = -1 (-1,0) Y Intercept 4(0) + y = -4 y = -4 (0, -4) x + 3y = 12 X Intercept x + 3(0) = 12 x = 12 (12,0) Y Intercept 0 + 3y = 12 3y = 12 y = 4 (0,4)

IV. Find the x and y intercepts. x + ½ y = -2 * X Intercept Y Intercept

V. Vertical Lines vs. Horizontal Lines A horizontal line is a line that has a slope of zero. Y = # is a horizontal line. A vertical line is a line that has an undefined slope. X = # is a vertical line. X = -2 Vertical Line Undefined Slope Y = 2 Horizontal Line Zero Slope Horizontal Line Zero Slope Y = 9

VI. Write an equation in slope intercept form for each line. Ex 1. A line passing through ( 2, 4) with a slope of ½. 4 = ½ (2) + B 4 = 1 + B 3 = B Y = ½ x + 3 Ex 2. A line with a slope of zero passing through (-2, -6). Zero slope means it’s a horizontal line so y = # Y = -6

VI. Write an equation in slope intercept form for each line. Ex 3. A line passing through (0, -1) and (2,2). Find the slope. M = 3/2 Plug slope and 1 of the above points into y = mx + b. -1 = 3/2(0) + B -1 = B Y = 3/2x -1

Writing Activities: Slopes and Intercepts 1a). In your own words, define the slope of a line. 1b). Give an example of three lines with the same slope.

Writing Activities: Slopes and Intercepts 2a). In your own words, define the y-intercept of a line. 2b). Give an example of three lines with the same y-intercept.

Writing Activities: Slopes and Intercepts 3). What are the characteristics of a line that has the equation y = mx? 4). What does the slope of a line indicate about the line? Include some examples. 5). Explain the difference between a line with a slope of 0 and a line with no slope.