Question

How do you graph the line $x + 4y = - 8$?

Answer 1

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.