Question

Please help me figure out the line Is it 4x + 2Y = 8

Answer 1

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.

`\begin{gathered} y=mx+b \\ x=0,y=4 \\ 4=0*m+b \\ 4=b \end{gathered}`

Then, the equation of the line is:

`y=mx+4`

Step 03: Substitute the second point in the equation.

`\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: \\ -(4)/(2)=(2)/(2)m \\ -2=m \end{gathered}`

Then, the equation of the line is:

`y=-2x+4`

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:

`\begin{gathered} y+2x=-2x+4+2x \\ y+2x=4 \\ \end{gathered}`

And multiply both sides by 2:

`\begin{gathered} (2x+y)*2=4*2 \\ 4x+2y=8 \end{gathered}`

Answer:

The equation of the line is:

y = -2x + 4

Which is the same as:

4x + 2y = 8