Question

Find the equation of the line passing through the point \[\left( { - 4,3} \right)\] with slope \[\dfrac{1}{2}\].

Answer 1

Hint: We have one point $( - 4,3)$ in the form of $({x_1},{y_1})$ and a slope to get the equation of a line. We will put the values of $({x_1},{y_1})$ and slope in the formula of the equation of line.

Formula used: Equation of a line \[y - {\text{ }}{y_1} = m\left( {x - {x_1}} \right)\]

Complete step by step answer:
(1) Let \[P\left( { - 4,3} \right)\] is a point through which line passes and \[m = \dfrac{1}{2}\] be its slope.
\[\therefore \] given point \[P\left( { - 4,3} \right)\], \[m = \dfrac{1}{2}\]
(2) We know that equation of a line passing through a point and having a slope is given as:
\[y - {y_1} = \,\,m(x - {x_1})\]
Here, m is slope of the line
\[\therefore m = \dfrac{1}{2}\]
(x1,y1) is the point through which it passes.
\[\therefore ({x_1},{y_1}) = P( - 4,3)\]
(3) Using value of P and m in formula mentioned in step (2)
\[
  (y - 3) = \dfrac{1}{2}\left( {x - ( - 4)} \right) \\
   \Rightarrow y - 3 = \dfrac{1}{2}(x + 4) \\
 \]
Cross multiplying the number, we have
$ \Rightarrow 2(y - 3) = (x + 4)$
\[ \Rightarrow 2y - 6 = x + 4\]
$ \Rightarrow x + 4 - 2y + 6 = 0$
\[ \Rightarrow x - 2y + 10 = 0\]
Which is the required equation of the line through point \[\left( { - 4,3} \right)\] having slope \[\dfrac{1}{2}\]

Additional Information: The slope of a line in the plane containing the x and y-axis is generally represented by the letter m, and is defined as the change in the y-coordinate divided by the corresponding change in the x-coordinate between two distinct points on the line.

Note: Slope is an angle that a line makes with positive x-axis measured anticlockwise. Students should be careful while doing the cross multiplication of the numbers.