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MA112 – 1.4 Equations of Lines ‘Finding the line from data’ Today: 1.4: finding the equation for a line Announcements Homework 1.4 due Fri Module 1 quiz (today / Fri) quiz next class: find equation of the line through 2 points A. Line: Simplest Relationship Between x and y Geometrically, a line can be defined by any 2 distinct points. Equivalentially, a line can be defined by one point and a direction. Ingredients for a line: a point (place to start) a direction (where to go from there) The ‘direction’ can be provided by another point. Different Ways of Describing Lines Slope-Intercept Form Point-Slope Equation y mx b m = slope (0,b) = y-intercept direction! point! y y1 mx x1 m = slope (x1,x2) = arbitrary point weirder ones: intercept-intercept and parametric In this section, we will focus on slope-intercept form: y mx b . Finding a line given data (1) find the slope of the line (find m) (2) find the y-intercept (find (0,b)) by plugging in any known point (3) write y mx b Parallel and Perpendicular Two lines are parallel if they have the same slope. (If they go through different points, they are two different lines.) Two lines are perpendicular if they have opposite slopes. (Their slopes are negative reciprocal of one another.) 1 x 7 are perpendicular. 2 y 2 x 10 and y find a || or using the line’s slope and a given point