To find the equation of a line let's use the generic equation in the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
To find the equation of the line, follow the steps below.
Step 01: Find 2 points in the graph.
Finding 2 points (x, y) in the graph:
(0, 4) and (2, 0).
Step 02: Substitute the first point in the equation.
[tex]\begin{gathered} y=mx+b \\ x=0,y=4 \\ 4=0*m+b \\ 4=b \end{gathered}[/tex]
Then, the equation of the line is:
[tex]y=mx+4[/tex]
Step 03: Substitute the second point in the equation.
[tex]\begin{gathered} y=mx+4 \\ x=2,y=0 \\ 0=m*2+4 \\ 0=2m+4 \\ Subtracting\text{ }4\text{ }from\text{ }both\text{ }sides: \\ 0-4=2m+4-4 \\ -4=2m \\ Dividing\text{ }both\text{ }sides\text{ }by\text{ }2: \\ -\frac{4}{2}=\frac{2}{2}m \\ -2=m \end{gathered}[/tex]
Then, the equation of the line is:
[tex]y=-2x+4[/tex]
The equation of the line in the slope-intercept form is: y = -2x + 4
Step 04: Compare with the given equation:
To do it, add 2x to both sides:
[tex]\begin{gathered} y+2x=-2x+4+2x \\ y+2x=4 \\ \end{gathered}[/tex]
And multiply both sides by 2:
[tex]\begin{gathered} (2x+y)*2=4*2 \\ 4x+2y=8 \end{gathered}[/tex]
Answer:
The equation of the line is:
y = -2x + 4
Which is the same as:
4x + 2y = 8
