Correct the error:
Question: Find the point-slope equation of the line with slope -3 that passes through the point (2,-10).
Solution: y-y^1=m(x-y^1)
y-(2)=-3(x-(-10)
y-2=-3(x+10)
the eqation 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 sign of the slope is incorrect. The slope is given as -3, but in the solution, it is used as 3.
To solve the problem correctly, we can use the point-slope formula:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope.
Using the values from the given point (2, -10) and the correct slope (-3), the correct equation would be:
y - (-10) = -3(x - 2)
Simplifying this equation gives:
y + 10 = -3x + 6
Therefore, the correct equation of the line is:
y = -3x - 4