MHB Finding the Constant a for a Given Point on a Linear Equation

AI Thread Summary
To find the constant a for the equation y = -5x - a that passes through the point (-4, 1), substitute x and y into the equation. This leads to the equation 1 = 20 - a, which simplifies to a = 19. The solution is verified by substituting a back into the equation, confirming that y equals 1 when x is -4. The discussion emphasizes the method of substitution and verification for linear equations. The approach is effective for similar problems involving linear equations and points.
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You are given an equation and a point. In each case, find the value of the constant a so that the graph of the equation passes through the given point.

y = -5x - a; (-4, 1)

Solution:

Let x = -4 and y = 1

y = -5x - a

1 = -5(-4) - a

1 = 20 - a

1 - 20 = - a

-19 = -a

-19/-1 = a

19 = a

Correct?
 
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RTCNTC said:
You are given an equation and a point. In each case, find the value of the constant a so that the graph of the equation passes through the given point.

y = -5x - a; (-4, 1)

Solution:

Let x = -4 and y = 1

y = -5x - a

1 = -5(-4) - a

1 = 20 - a

1 - 20 = - a

-19 = -a

-19/-1 = a

19 = a

Correct?

The answer is right. to check the correctness of the result you can put the value and check

$y= -5x - 19$ and at $x = -4 $ we get $y= - 5 * (-4) -19 = 20-19 =1$ which is true
 
Very interesting. I will do likewise for the other question.
 
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