Question

Write the equation of the line $x+2y-4=0$ in the slope intercept form and then find the slope and the y intercept of the line.

Answer 1

Hint: In this question, we will write the given equation in terms of general slope intercept form and then by comparison we will find slope and y-intercept of the given line.
Complete step-by-step answer:
In two-dimensional geometry, equation of line in slope intercept form can be written as,
$y=mx+c$
Where x is value of x coordinate, and y is value of y coordinate.
Here, m represents the slope of the lines and c represents the y intercept of the line.
In a line, slope of line is the value of tangent function for the angle which a given line makes with the x-axis in the anticlockwise direction.
And, y-intercept of a line is the point on the y-axis. The given line intersects the y axis.
Now, the given line in a question is,
$x+2y-4=0$
Adding 4 on both sides of the equation, we get
$x+2y=4$
Subtracting x from both sides of the equation, we get,
$2y=4-x$
Dividing both sides of the equation by 2, we get,
$\begin{aligned} & \dfrac{2y}{2}=\dfrac{4-x}{2} \\\ & \Rightarrow y=\dfrac{4}{2}-\dfrac{x}{2} \\\ & \Rightarrow y=\left( \dfrac{-1}{2} \right)x+2 \\\ \end{aligned}$
This is an equation of line $x+2y-4=0$ in slope intercept form. Comparing this equation with general form of slope intercept form $y=mx+c$, we get:
$m=\left( \dfrac{-1}{2} \right),\,\,\,c=2$
Hence, the slope of the given line is $\dfrac{-1}{2}$ and y-intercept of the line is 2.
Note: In this type of question, if any term of slope intercept form is not present, then we write it to be zero.