Lesson 2 The Straight Line.docx - Lesson 2 The Straight Line Objectives At the end of the lesson you should be able to 1 find the equation of a line a

# Lesson 2 The Straight Line.docx - Lesson 2 The Straight...

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Lesson 2. The Straight Line Objectives . At the end of the lesson, you should be able to: 1. find the equation of a line a. that is parallel or perpendicular to an axis b. using point-slope form c. using slope-intercept form d. using intercept form 2. reduce a given equation of a line to standard forms 3. determine the slope, x-intercept, and y-intercept of a line with a given equation 4. find the equation of a line that is parallel or perpendicular to a given line 5. draw a line given its equation What is the shortest path between two points? The answer is a straight line . A straight line may be referred to simply as a line. Lines Parallel to an Axis If a line is parallel to and at a directed distance x 1 from the y-axis, its equation is x = x 1 . If the line is parallel to and at a directed distance y 1 from the x-axis, its equation is y = y 1 . Example . Give the equation of the line 1. through (2, -3) and parallel to the x-axis 2. through (1/2, 7) and perpendicular to the x-axis 3. through (-11/3, 5) and parallel to the y-axis 4. through (5, -10/3) and perpendicular to the y-axis General Equation of a Line The general equation of the first degree in x and y is also the general equation of a line. It is of the form Ax + By + C = 0 . O P( x 1 , y 1 ) x = x 1 y = y 1 y x y = 1 x = -3 O

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Standard Equations of a Straight Line A. Point – Slope Form Suppose a line l whose equation is to be found, passes through the point P 1 ( x 1 , y 1 ) and has slope equal to m. Take any point P(x, y) on the line. By slope formula, m = y y 1 x x 1 . Simplifying, we obtain the point-slope form of a line y y 1 = m ( x x 1 ) Examples 1. Find the general equation of the line a. Through (-2, 5) ,with slope 3 b. Through (3, 7), with slope 5/2 c. Through (-9/2, 4), with slope -7/3 2. A line passes through (2, -5) and makes an angle of 45 with the x-axis. Find its equation.
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• jane smeth

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