Question

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

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, now we will have to 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 \[y = - 4x + 4\] .So when \[x = 0\] we get So when \[x = 0\]we get,
\[
\Rightarrow y = 0 + 4 \\
\Rightarrow y = 4 \\
\]
Therefore, we get the y-intercept as 4. The line will cut the Y-axis at point 4.
Now we will select the point y=0.
\[
\Rightarrow 0 = - 4x + 4 \\
\Rightarrow 4x = 4 \\
\Rightarrow x = 1 \\
\]
Therefore, we get x-intercept as 1. The line will cut x-axis at 1.

Hence, we plot the points (0,4) and (1,0) on the graph and the line is plotted by joining these points.

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