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Warm Up 1. Determine if this relation is a function. 2. Find π(3) if π π₯ = π₯ 2 β2 . π₯β1 3. Find the x-intercept and y-intercept of the graph of 3π₯ β 5π¦ = 15. The graph the equation. 4. Find the slope of a line that passes through (3, 5) and (4, 1). 2.4 Writing Equations of Lines The slope intercept form of the equation of a line is π¦ = ππ₯ + π where π is the ___________ and π is the _____________. Slope-Intercept Form If you are given the slope and y-intercept of a line, you can find an equation of the line by substituting the values of π and π into the slope-intercept form. 1. π ππππ 4 , πππ π ππ 3 π‘βπππ’πβ 0, 4 Examples Sometimes it is necessary to calculate the slope before you can write an equation. Write an equation in slope-intercept form for the line. Try two on your own. Write an equation of the line. 1. πππ π ππ π‘βπππ’πβ 0, β6 πππ β4, 10 . 2. πππ π ππ π‘βπππ’πβ 6, β2 π€ππ‘β π π ππππ ππ β 4. Point-Slope Form The point-slope form of the equation of a line is π¦ β π¦1 = π(π₯ β π₯1 ), where (π₯1 , π¦1 ) are the coordinates of a point on the line and π is the slope of the line. Using a previous example: Write an equation of a line through 6, β2 with a slope of 4 using point-slope form. Try two on your own. Write an equation of the line. 1. πππ π ππ π‘βπππ’πβ 2, 3 π€ππ‘β π π ππππ ππ 1 2 2. πππ π ππ π‘βπππ’πβ β2, β1 π€ππ‘β π π ππππ ππ β 3. Standardized Testing Tests like HSAP or the COMPASS love to ask questions like thisβ¦ Which is an equation of the line that passes through (-2, 7) and (3, -3)? A. π = π π π β π π B. π = βππ + π C. π = π π π +π D. π = ππ + ππ Equations of a Line What if you are asked to write the equation of a line given two points? (-8, -5) and (-3, 10) What would you have to do? 1. Find the SLOPE (π) 2. Use point-slope form to find the equation Parallel Lines How do you know if two lines are parallel? Their SLOPES are the SAME! π¦ = 3π₯ β 1 and π¦ = 3π₯ + 13 π¦= 1 π₯ 2 and π¦ = 1 π₯ 2 +1 Example Write an equation of a line that passes through π (12, 0) and is parallel to π = β π β π. π Write an equation of a line that passes through (0, 9) π and is parallel to π = π β ππ. π Perpendicular Lines How do you know if two lines are perpendicular? Their SLOPES are the NEGATIVE RECIPROCALS! π¦ = 3π₯ β 1 and π¦ = π¦ = β2π₯ and π¦ = 1 β π₯ 3 1 π₯ 2 + 13 +1 Example Write an equation of a line that passes through π (5, -6) and is perpendicular to π = β π + π. π Write an equation of a line that passes through (6, -1) and is parallel to π = ππ β π. Summary Slope-Intercept Form: Point-Slope Form: Equations of a line: (1) (2) Parallel Lines: Perpendicular Lines: Homework!!! YAY! ο Lesson 2.4 Page 87 #βs 9, 13, 15, 17-19, 23, 24 and 32