Clare was solving an equation, but when she checked her answer she saw her solution was incorrect. She knows she made a mistake,
but she can't find it. Place the box over the two lines where Clare made her mistake and solve for the solution to the equation?
2 answers:
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- Zero Product Property: if a × b = 0, then either a or b = 0 or both a and b = 0.
(Make sure to set f(x) to zero)
So for this equation, I will be factoring by grouping. Firstly, what two terms have a product of -5x^2 and a sum of 4x? That would be 5x and -x. Replace 4x with 5x - x:
Next, factor 5x^2 + 5x and -x - 1 separately. Make sure that they have the same quantity on the inside:
Now you can rewrite the equation as:
Now apply zero product property to the factors to solve for x:
<u>The x-intercepts are (1/5 ,0) and (-1,0).</u>
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Answer:
5x -y = -37
Step-by-step explanation:
One way to find the coefficients A and B is to use the differences of the x- and y-coordinates:
A = Δy = y2 -y1 = 2 -(-3) = 5
B = -Δx = -(x2 -x1) = -(-7 -(-8)) = -1
Then the constant C can be found using either point.
5x -y = 5(-7) -2 = -37
The equation of the line is ...
5x -y = -37
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<em>Additional comment</em>
This approach comes from the fact that the slope of a line is the same everywhere.
The "standard form" requires that A be positive, so we chose point 1 and point 2 to make sure that was the case.
