Question

How do you graph the line \[x + 4y = - 8\]?

Answer 1

Hint:In the above question, we need to plot the above line on the graph. Since, the given equation is a line where the equation of the straight line is \[y = mx + c\] so we can compare with this equation and find out the coordinates of the line on the cartesian plane.

Complete step by step solution:
In the above equation, we have to plot the line on the graph. To find the coordinates of the line what we can do is to select some values of x coordinate and then evaluate those values in the given equation.
So, we will select a value for x i.e., zero and we substitute the value in \[y = mx + c\]
where m is the slope and c is the constant term y-intercept. So, substitute the value in equation we get,
The equation is \[x + 4y = - 8\].So when \[x = 0\] we get,
\[
\Rightarrow 0 + 4y = - 8 \\
\Rightarrow y = \dfrac{{ - 8}}{4} = - 2 \\
\]
Therefore, we get the y-intercept as -2. The line will cut the Y-axis at the point -2.
Now we will select the point y=0.
\[
\Rightarrow x + 4\left( 0 \right) = - 8 \\
\Rightarrow x = - 8 \\
\]
Therefore, we get x-intercept as -8. The line will cut x-axis at -8.

Therefore, we get the points x-intercept and y-intercept which explains that cuts X-axis and Y axis respectively so that lines can be formed by joining the points.

Note: An important thing to note is that slope contains the direction in which you go from one point to another. where .\[m = \dfrac{y}{x} \Rightarrow \dfrac{{rise}}{{run}}\]..The numerator tells you many steps to go up and down and denominators tell us how many steps to move left or right.