Question

when will this equation intersect on a graph :−5/2x−1=4x+2
?

Answer 1

To find the intersection point of the two equations given, we need to solve the equation you've provided:

\[
-\frac{5}{2}x - 1 = 4x + 2.
\]

First, let's rearrange the equation to isolate terms involving \(x\) on one side.

1. Start by adding \(5/2x\) to both sides to get all \(x\) terms on one side:

\[
-1 = 4x + \frac{5}{2}x + 2.
\]

2. Now, combine the \(x\) terms on the right. The term \(4x\) can be expressed as \(\frac{8}{2}x\) to have a common denominator:

\[
-1 = \frac{8}{2}x + \frac{5}{2}x + 2.
\]

3. Combining the two fractions gives:

\[
-1 = \frac{13}{2}x + 2.
\]

4. Next, subtract 2 from both sides:

\[
-1 - 2 = \frac{13}{2}x,
\]

which simplifies to:

\[
-3 = \frac{13}{2}x.
\]

5. To solve for \(x\), multiply both sides by \(\frac{2}{13}\):

\[
x = -3 \cdot \frac{2}{13} = -\frac{6}{13}.
\]

Now that we have \(x\), we can find the \(y\) value by substituting \(x\) back into either of the original equations. We'll use the second equation \(y = 4x + 2\):

\[
y = 4\left(-\frac{6}{13}\right) + 2 = -\frac{24}{13} + 2 = -\frac{24}{13} + \frac{26}{13} = \frac{2}{13}.
\]

Thus, the point of intersection of the two equations is:

\[
\left(-\frac{6}{13}, \frac{2}{13}\right).
\]

This is where the two graphs will intersect.

Answer 2

I need you to answer in graph form. Example: (?,?)

Answer 3

The intersection point of the equations is \(\left(-\frac{6}{13}, \frac{2}{13}\right)\).

In graph form, this can be expressed as:

\[
\left(-\frac{6}{13}, \frac{2}{13}\right)
\] or approximately \((-0.46, 0.15)\) if you prefer decimal values.