What is the point-slope form of a line with slope 6 that contains the point $(1,2)$?
A. $y-2=6(x-1)$
B. $y+2=6(x-1)$
C. $y+2=6(x+1)$
D. $x+1=6(y+2)$
Answer (1)
Recall the point-slope form: y − y 1 = m ( x − x 1 ) .
Substitute the given slope m = 6 and point ( 1 , 2 ) into the formula: y − 2 = 6 ( x − 1 ) .
The point-slope form of the line is y − 2 = 6 ( x − 1 ) .
Explanation
Understanding the Problem We are given a line with a slope of 6 that passes through the point (1, 2). Our goal is to find the equation of this line in point-slope form.
Recalling Point-Slope Form The point-slope form of a line is given by the equation: y − y 1 = m ( x − x 1 ) where m is the slope of the line and ( x 1 , y 1 ) is a point on the line.
Substituting Values We are given that the slope m = 6 and the point ( x 1 , y 1 ) = ( 1 , 2 ) . Substituting these values into the point-slope form, we get: y − 2 = 6 ( x − 1 )
Identifying the Correct Option Comparing our equation y − 2 = 6 ( x − 1 ) with the given options, we see that it matches option A.
Final Answer Therefore, the point-slope form of the line with slope 6 that contains the point (1, 2) is y − 2 = 6 ( x − 1 ) .
Examples
Point-slope form is useful in many real-world scenarios. For example, if you know the rate at which you are saving money (your slope) and how much you have saved at a certain time (a point), you can use the point-slope form to determine how much money you will have saved at any given time in the future. Similarly, in physics, if you know the velocity of an object at a particular time and its constant acceleration, you can use the point-slope form to determine its velocity at any other time.
