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.
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.
The error in the solution is that the point-slope equation of a line is in the form y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
To solve the problem correctly, we need to use the given slope of -3 and the point (2, -10).
The correct solution is:
Step 1: Plug in the values of the given point into the point-slope equation:
y - (-10) = -3(x - 2)
Step 2: Simplify the equation:
y + 10 = -3x + 6
Step 3: Rearrange the equation to the slope-intercept form (y = mx + b):
y = -3x + 6 - 10
y = -3x - 4
Hence, the correct point-slope equation of the line with slope -3 that passes through the point (2, -10) is y = -3x - 4.
The error in the solution is that it did not correctly find the point-slope equation of the line with the given information.
To correctly solve this 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) represents the coordinates of a point on the line, and m represents the slope of the line.
In this case, the given point is (2, -10) and the slope is -3.
To find the point-slope equation, we substitute these values into the formula:
y - (-10) = -3(x - 2)
Simplifying further:
y + 10 = -3x + 6
This is the correct point-slope equation for the line with a slope of -3 that passes through the point (2, -10).