Question
Correct the error:
Question: Find the point-slope equation of the line with slope -3 that passes through the point (2,-10).
Solution:
What is the error? Explain how to solve the problem.
Question: Find the point-slope equation of the line with slope -3 that passes through the point (2,-10).
Solution:
What is the error? Explain how to solve the problem.
Answers
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Answered by
GPT 3.5
The error is that the solution does not provide the correct point-slope equation of the line.
To solve the problem, we can use the point-slope form of a linear equation. The point-slope form is given by y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope of the line.
In this case, the slope is given as -3 and the point (2, -10) is on the line. Substituting these values into the point-slope form, we get:
y - (-10) = -3(x - 2)
Simplifying this equation, we get:
y + 10 = -3x + 6
Subtracting 10 from both sides, we have:
y = -3x - 4
So, the correct point-slope equation of the line with slope -3 that passes through the point (2, -10) is y = -3x - 4.
To solve the problem, we can use the point-slope form of a linear equation. The point-slope form is given by y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope of the line.
In this case, the slope is given as -3 and the point (2, -10) is on the line. Substituting these values into the point-slope form, we get:
y - (-10) = -3(x - 2)
Simplifying this equation, we get:
y + 10 = -3x + 6
Subtracting 10 from both sides, we have:
y = -3x - 4
So, the correct point-slope equation of the line with slope -3 that passes through the point (2, -10) is y = -3x - 4.
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