Where’s the fire? A fire station is located on a grid at (-3,2) and sights a fire along a line of sight with a slope of. Another fire station located.

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Presentation transcript:

Where’s the fire?

A fire station is located on a grid at (-3,2) and sights a fire along a line of sight with a slope of. Another fire station located on the same grid at (9,1) sights the same fire along a line of sight with a slope of.

Where’s the fire? What are the coordinates of the fire? What are the equations of the sight lines? Use graphing to obtain the coordinates of the fire and verify with an algebraic solution.

(-3,2) (9,1) (3,5)

Point – Slope Form y - y 1 = m(x – x 1 )

Standard Form ax +by = c 2(y – 2) = 1 (x +3) 2y – 4 = x + 3 -x + 2y = 7 x - 2y = -7

Standard Form ax + by = c 3(y -1) = -2(x – 9) 3y – 3 = -2x x + 3y = 21

Elimination x - 2y = -7 2x + 3y = 21 -7y = -35 y = 5 x - 2(5) = -7 x - 10 = -7 x = 3 The fire is at (3,5) 2x - 4y = -14 2x + 3y = 21(-) Times 2

Slope – Intercept Form y = mx + b

Substitution = Multiply both sides by 6 3x +21 = -4x x =21 x= 3 y = 5