Question

How do you write an equation given a slope of \[\dfrac{1}{2}\] and the point \[\left( { - 2,7} \right)?\]

Answer 1

Hint: The given question describes the operation of addition/ subtraction/ multiplication/ division. We need to know the formula for point-slope form. Also, we need to know which one is the slope and which one is \[\left( {{x_1},{y_1}} \right)\] in the formula of point-slope form. The final answer should be an equation with the involvement of variables \[x\] and \[y\] . We need to identify which is \[m\] and which is \[\left( {{x_1},{y_1}} \right)\] in the given question.

Complete step-by-step answer:
In the given question we would write an equation for the given slope \[\dfrac{1}{2}\] and given point \[\left( { - 2,7} \right)\] . So, we have a slope and point on a given question.
The formula for the point-slope form is given below,
 \[\left( {y - {y_1}} \right) = m \cdot \left( {x - {x_1}} \right) \to \left( 1 \right)\]
Here, \[m\] is the slope of \[y\] and \[\left( {{x_1},{y_1}} \right)\] is the point.
From the question we have a slope \[\dfrac{1}{2}\] so, the value of \[m\] is \[\dfrac{1}{2}\] and we have \[\left( { - 2,7} \right)\] , so the value of \[\left( {{x_1},{y_1}} \right)\] is \[\left( { - 2,7} \right)\] .
Let’s substitute the values of \[m\] and \[\left( {{x_1},{y_1}} \right)\] in the equation \[\left( 1 \right)\] , we get
 \[\left( 1 \right) \to \left( {y - {y_1}} \right) = m \cdot \left( {x - {x_1}} \right)\]
 \[\left( {y - 7} \right) = \dfrac{1}{2}\left( {x + 2} \right)\]
By solving the above equation, we get
 \[
  2\left( {y - 7} \right) = \left( {x + 2} \right) \\
  2y - 14 = x + 2 \\
 \]
Let’s separate the constant terms in the above equation, so we get
 \[
  2y - x = 2 + 14 \\
  2y - x = 16 \\
  0 = x - 2y + 16 \\
 \]
So, the final answer is,
 \[x - 2y + 16 = 0\]
So, the correct answer is “ \[x - 2y + 16 = 0\] ”.

Note: Remember the formula for the slope-point form to solve these types of questions. Also, we would know which is slope and point in the equation. Note that in these types of questions we would consider the given point as \[\left( {{x_1},{y_1}} \right)\] . Note that the final answer would be an equation with the involvement of \[x\] \[y\] and constant terms. This type of question also involves the operation of addition/ subtraction/ multiplication/ division.