Standard Form of a Linear Equation Ax + By = C where: 1) A, B, and C
are integer coefficients... AND N.B. If either A or B is zero, you have a special linear equation in either vertical line form (i.e. x = 3) or horizontal line form (i.e. y = -7). How to solve for STANDARD FORM: 1) ISOLATE the CONSTANT (to the right side of the "=" sign) 2) FRAC-ATTACK - Eliminate fractional coefficients using the LCD Example: y = - 3/5 x + 3 << add 3/5 x to both sides >> 3/5 x + y = 3 << Multiply both sides by LCD (5) >> 3x + 5y = 15 woo-hoo! that's all folks! Standard Form is considered useful for finding quick graphs using intercepts. Hmmm... up 'til now, haven't we called this "intercept form?" Can you find the coordinates for the x- and y-intercepts for the equation we developed above?
Convert to STANDARD FORM: 1) y = 3x + 1 2) y = - 3/4 x - 4 3) y = 7/2 x + 1/4 4) Challenge! (3, 2) (6, 3)
Example Problem: 1) -3x + y = 1 2) -3x - 4y = 16 3) -14x + 4y = 1 4) m = 1/3; y = 1/3x + 1; -x + 3y = 3
Challenge Problem #1: Larry runs at an average rate of 8 mi/hr. He walks at a rate of 3 mi/hr. Let x represent the time spent running and y represent the time spent walking. a) Write a linear equation in standard form to relate the times he could spend running and walking if he travels a distance of 15 miles. b) graph the line in the coordinate plane. c) convert the equation to slope-intercept form.
Challenge Problem #2: The 8th grade class holds a car wash to raise money for the Washington trip. A local merchant donates all of the supplies. A car wash costs $5 and a van/SUV wash costs $7.50. Let x represent the number of cars and y represent the number of vans/SUVs. a) Write a linear equation in standard form to relate the number of cars and/or vans/SUVs that the students must wash to raise $900. b) graph the line in the coordinate plane. c) convert the equation to slope-intercept form.
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