Question

How do you graph $y = 2x + 4$?

Answer 1

Hint: In this problem we have given a linear equation and we are asked to draw the graph of the given equation. To draw the graph of the given equation first we want to find the slope and $y$ intercept of the given equation and also we find the points for the given equation and using those points only we are going to plot the graph.

Formula used: The slope intercept form is $y = mx + b$, where $m$ is the slope value and $b$ is the is the $y$ intercept.

Complete step-by-step solution:
Given equation is $y = 2x + 4$
Now, let’s compare the given equation with the slope intercept form.
$m = 2$ and $b = 4$
The slope of the line is the value of $m$, and the $y$ intercept is the value of $b$.
Slope: $2$
$y$- intercept: $4$
Any line can be graphed using two points. So select two values for $x$, and plug them into the equation to find the corresponding $y$ values.
Choose $0$ to substitute in for $x$ to find the ordered pair.
Replace the variable $x$ with $0$ in the expression.
$ \Rightarrow f\left( 0 \right) = 2\left( 0 \right) + 4$
$ \Rightarrow f\left( 0 \right) = 4$
The $y$ value at $x = 0$ is $4$
$ \Rightarrow y = 4$
Choose $1$ to substitute in for $x$ to find an ordered pair.
Replace the variable $x$ with $1$ in the expression.
$ \Rightarrow f\left( 1 \right) = 2\left( 1 \right) + 4$
Simplify the result.
$ \Rightarrow f\left( 1 \right) = 2 + 4 = 6$
The final answer is $6$.
The $y$ value at $x = 1$ is $6$.
$ \Rightarrow y = 6$
Graph the line using the slope and the $y$- intercept or the points,
Slope: $2$
$y$- intercept: $4$
The points: $\left( {0,4} \right),\left( {1,6} \right)$
The graph for the given equation using the above points is

Note: There are three basic methods of graphing linear functions. The first is by plotting points and then drawing a line through the points. The second is by using the $y$- intercept and slope. The third is applying transformations to the identity function $f\left( x \right) = xf\left( x \right) = x$. In this problem we used the first method to draw the graph for the given linear equation. The graph of $y = 2x + 1$ is a straight line. When $x$ increases, $y$ increases twice as fast.