Correct the error:
Question: Find the point-slope equation of the line with slope -3 that passes through the point (2,-10).
Solution:
y-y1=m(x-x1)
y-2=-3(x-(-10))
y-2=-3(x+10)
the equation of the line is y-2=-3(x+10)
What is the error? Explain how to solve the problem.
The error in the solution is that the point (-10) in the equation of the line is incorrect. The correct point is (2, -10), not (x, -10).
To solve the problem correctly, you should substitute the correct coordinates of the given point into the equation.
The correct solution should be:
y - y1 = m(x - x1)
y - (-10) = -3(x - 2)
y + 10 = -3x + 6
Therefore, the correct equation of the line is y + 10 = -3x + 6.
The error in the solution provided is the choice of the point (2, -10) as (x1, y1) in the equation. The correct coordinates for the point are (x1, y1) = (2, -10), but in the solution, the point is mistakenly written as (y1, x1) = (-10, 2).
To solve the problem correctly, you need to use the correct coordinates for the point in the point-slope form equation. Here's the correct solution:
Given slope (m) = -3 and point (x1, y1) = (2, -10).
The point-slope form equation is:
y - y1 = m(x - x1)
Substituting the values, we have:
y - (-10) = -3(x - 2)
y + 10 = -3x + 6
Rearranging the equation to the standard form:
3x + y = -4
Therefore, the correct equation of the line with a slope of -3 passing through the point (2, -10) is 3x + y = -4.
The error in the solution is that the point (2,-10) was incorrectly entered as (x1, y1) instead of (x1, y1).
To correct the error and solve the problem, we need to use the correct coordinates of the point (2,-10).
The correct solution would be:
y - y1 = m(x - x1)
y - (-10) = -3(x - 2)
y + 10 = -3(x - 2)
y + 10 = -3x + 6
y = -3x - 4
Therefore, the correct point-slope equation of the line with slope -3 passing through the point (2,-10) is y = -3x - 4.