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Write an equation of a line by using the slope and a point on the line. Point-Slope Form Uses one point, (x1, y1) on a line to create an equation Writing an Equation A line passes through (-3, 6) and has a slope of -5. 𝑦 − 𝑦1 = m(𝑥 − 𝑥1 ) Plug in the slope an d point 𝑦 − 6 = -5(𝑥 − (−3)) y – 6 = -5(x + 3) Graphing y–1= 2 (x 3 – 2) 2 3 We know the slope is And it passes through the point (2, 1) Standard Form of a Linear Equation So far we have learned how to write linear equations in slope-intercept form and point-slope form. Standard form is written Ax + By = C where A, B, and C are real numbers Intercepts The x-intercept is the x-coordinate of a point where a graph crosses the x-axis. Found where the y-value is 0 Find x and y intercepts of the graph of 3x + 4y = 24 Sub 0 for y to find x-intercept X =8 Sub 0 for x to find y-intercept Y=6 Graphing Using Intercepts What is the graph of x – 2y = -2? Find intercepts X = -2 Y=1 Write as ordered pairs (-2, 0) (0, 1) Plot the ordered pairs Horizontal and Vertical Lines x=3 Write in standard form: 1x + 0y = 3 y=3 Standard form: 0x + 1y = 3 Transforming to Standard Form 3 − 𝑥 7 + 5 in standard form What is y = Get rid of fractions by multiplying by 7 7y = 3 7(− 𝑥 7 + 5) Distribute: 7y = -3x + 35 Add 3x: 7y + 3x = 35 Done! These equations, though they look different, are equivalent. Parallel Lines Lines in the same plane that never intersect. Nonvertical lines are parallel if they have the same slope and different y-intercepts. Vertical lines are parallel if they have different x-intercepts. Ex: Same slope, different y-intercept Perpendicular lines Lines that intersect to form right angles Two nonvertical lines are perpendicular if the product of their slopes is -1. The slope is the opposite reciprocal. Ex: the opposite reciprocal of 3 − 4 4 3 is since their product is -1. A vertical line and a horizontal line are always perpendicular.