1.4 Lines, writing, finding slopes and intersections Part I Line on a graph: Count up(+)/down(-) and right(+)/left(-) from one point on the line to another and simplify. Example: Practice: -3/2 y goes down 3 as x goes right 2 2/3 y goes up 2 while x goes right 3

1.4 Lines, writing, finding slopes and intersections Part I Given points: use the equation (difference in y’s over difference in x’s) Example: Practice: (-2,1); (0,0) (-2,3); (2,1)

1.4 Lines, writing, finding slopes and intersections Part I Given an equation: solve for y, then the coefficient of x is the slope. Example: Practice: y – 3 = 2x + 5 3y = 2x + 6 y = 2x + 8 m = 2 slope y = 2/3 x + 2 m = 2/3 slope

Special cases: Vertical line: The equation is written as x = a (there is no y because it never crosses the y axis) the slope is undefined. x = 5 is a vertical line going through the x axis at 5 and the slope is undefined because the denominator is 0 Horizontal: The equation is written as y = b (there is no x because it never crosses the x axis) the slope is 0 y = -3 is a horizontal line going through the y axis at -3 and the slope is 0 because the numerator is 0.

Writing the equation of a line: 3 formulas: Slope intercept form: y = mx + b slope y value of the y intercept point Example: write the equation of the line with a slope of -3 and a y-intercept at 4. y = -3x + 4 Practice: write the equation of a line through the points (0,3); (4,4) First find the slope: the y-intercept is 3 since one of the points has a 0 for x the y value must be the y intercept. y = ¼ x + 3

Writing the equation of a line: slope Point slope form: y – y1 = m(x – x1) y value of x value of a a point point Example: write the equation of a line whose slope is – ½ and goes through a point (4, -2). y - -2 = - ½ (x – 4) ; y + 2 = - ½ (x – 4) Practice: write the equation of the line that goes through (2,5) & (-3,4) Find slope then use either point to finish the equation. y – 5 = 1/5(x – 2)

Standard form: Ax + By = C Conditions: A has to be positive (coefficient of x) A,B,C must be integers. Example: y = ½ x -4 2y = x – 8 -x +2y = -8 X – 2y = 8

Comparisons of slopes: // parallel lines must have the same slope but a different y-intercept Example: write the equation of a line Parallel to the line y = - ¼ x + 9 and through point (-1,7). Perpendicular lines must have opposite and reciprocal slope. (sign) (flip) Example: write the equation of a line perpendicular to the line y + 2 = 3/2 (x – 4) and through point (0,-3). Since the line is parallel the slope must be the same – ¼ and using point (-1,7) the equation is y – 7 = - ¼ (x + 1) Since the line is perpendicular the slope is opposite and reciprocal so it must be – 2/3 and using point (0,-3) the equation is y = -2/3 x – 3

Practice: Write the equation of the line with the given properties using either form. #51) Slope = -3 ; y-intercept = 3 #63) Parallel to the line x = 5; containing the point (4,2) Find the slope and y-intercepts and graph #78)-x + 3y = 6 y = -3x + 3 x = 4 m = 1/3 (0, 2)