G RAPHING E QUATIONS & E QUATIONS OF L INES Lesson 13.1 & 13.2.

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Presentation transcript:

G RAPHING E QUATIONS & E QUATIONS OF L INES Lesson 13.1 & 13.2

S TRATEGIES TO G RAPH A L INE Make a table. Special lines Vertical lines Horizontal Lines Intercepts (x, 0) & (0, y) Slope-intercept form

M AKE A T ABLE & G RAPH 2 X – 4 Y = 10 x012 y -3 -5/2-5/2 -2-3/2-3/2

S PECIAL LINES : G RAPH Y = 4 & X = -2 y = 4 is a horizontal line where all the y values are 4. x = -2 is a vertical line where all of the x values are -2.

I NTERCEPTS F IND THE X - AND Y - INTERCEPTS FOR THE LINE 2 X – 5 Y = 10, THEN GRAPH. X –intercept: What is x when y is zero? 2x – 5(0) = 10 x = 5 …. (5, 0) Y-intercept: What is y when x is zero? 2(0) – 5y = 10 y = -2 … (0, -2)

U SE S LOPE -I NTERCEPT F ORM TO G RAPH THE L INE Y = 2 X - 5. y = mx + b y & x are any point (x, y) that line on the line. m is the slope b is the y-intercept (0, b) In the equation y = 2x – 5, m = 2 b = (0, -5) Graph the y-intercept Graph the slope Connect the dots.

V ARIOUS F ORMS OF L INEAR E QUATIONS Slope-Intercept Form (y-form) y = mx + b Point-Slope Form y – y 1 = m(x – x 1 ) m = slope and (x 1, y 1 ) is a known point Standard Form (General Form) Ax + By = C

T HINGS NOT TO F ORGET ABOUT L INEAR E QUATIONS 1. Parallel Lines have the SAME slope but different y-intercepts. 2. Perpendicular lines have slopes that are negative reciprocals. 3. Vertical lines have a slope that is undefined. 4. Horizontal lines have a slope of zero. 5. Midpoint between two points is found using the formula: x 1 + x 2, y 1 + y 2 2 2