Question

How would I graph the line, 3x+4y= -4

Answer 1

Given the equation:

3x + 4y = -4

Let's graph the line that represents the equation above.

To grah the line, rewrite the equation in slope-intercet form:

y = mx + b

Where m is the slope and b is the y-intercept.

Rerite the equation for y:

3x + 4y = -4

Subtract 3x from both sides:

3x - 3x + 4y = -3x - 4

4y = -3x - 4

Divide all terms by 4:

`\begin{gathered} (4y)/(4)=-(3x)/(4)-(4)/(4) \\ \\ y=-(3)/(4)x-1 \end{gathered}`

The slope of the line is -3/4, while the y-intercept is at (0, -1).

Now, let's graph the line using 3 points.

• When x = -4:

Substitute -4 for x and solve for y

`\begin{gathered} y=-(3)/(4)\ast(-4)-1 \\ \\ y=3-1 \\ \\ y=2 \end{gathered}`

• When x = 0:

Substitute 0 for x and solve for y

`\begin{gathered} y=-(3)/(4)\ast(0)-1 \\ \\ y=-1 \end{gathered}`

• When x = 4:

Substitute 4 for x and solve for y

`\begin{gathered} y=-(3)/(4)\ast4-1 \\ \\ y=-3-1 \\ \\ y=-4 \end{gathered}`

Therefore, we have the following points:

(-4, 2), (0, -1) and (4, -4)

Plot the three points on the graph, then connect all 3 points using a straight edge.

We have the graph attached below: