MTH 100 The Slope of a Line Linear Equations In Two Variables

Objectives 1.Find the Slope of a Line. 2.Find the Slopes of Horizontal and Vertical Lines. 3.Find the Slope and y-intercept of a Line from an Equation. 4.Graph a Line Using the Slope and a Point. 5.Determine the Relationship between Two Lines. 6.Write the Equation of a Line from Given Information.

Objective 1 Given two points (x 1, y 1 ) and (x 2, y 2 ), the slope m of the line through the points is given by

Objective 1 Examples Find the slope of the line through the given pairs of points: 1.(9, 4) and (-3, 1) 2.(8, 2) and (8, -5) 3.(6, 7) and (0, 7)

Objective 2 Recall, from Section 2.4, that x = number is the equation of a vertical line and y = number is the equation of a horizontal line. Horizontal lines have zero, or 0, slope (see Example 3 on the previous slide). Vertical lines have undefined slope (see Example 2 on the previous slide).

Objectives 3 and 4 A linear equation in slope-intercept form is written as y = mx + b, where m is the slope of the line and b is the y-intercept. An equation in standard form can be converted to slope-intercept form by isolating y. The slope and y-intercept of a linear equation are sufficient information to graph the line. Actually, the slope and any point on the line will accomplish the same objective.

Objective 3 and 4 Examples Find the slope and y-intercept of each equation. Then graph the line. 1.y = 2x – 5 2.3x + 4y = 24 Graph the line with slope m = -3 and passes through the point (2, -1).

Objective 5 Two lines in the plane can interact in four different ways: 1.The lines can be parallel (the slopes will be equal but the y-intercepts will be different); 2.The lines can be coinciding (the slopes and y- intercepts will both be equal); 3.The lines can be intersecting and perpendicular (the product of the slopes will be equal to -1); 4.The lines can be intersecting and not perpendicular (the products of the slopes will not be equal to -1).

Objective 5 Examples Classify the following pairs of lines as parallel, coinciding, intersecting and perpendicular, or intersecting and not perpendicular:

Objective 6 We use point-slope form [y – y 1 = m(x – x 1 )] as a starting point to writing a linear equation in either standard form [Ax + By = C] or slope- intercept form [y = mx + b]. In order to use point-slope form, you must have the slope of the line (m) and a point (x 1, y 1 ) on the line. Beware of horizontal and vertical lines.

Objective 6 Examples Find the equation of the line, in both standard and slope-intercept form, with the given information: 1.Through (3, -8) and (5, -2); 2.With undefined slope passing through (1, 4); 3.Horizontal and passing through (-9, -6).