Question

Use the graph to solve -3/2x - 2 = -4x 3

Answer 1

Setting the equations equal:
`\(-(3)/(2)x - 2 = -4x + 3\).` After solving,
`\(x = 2\).` Substituting into either equation gives \(y = -5\). The point of intersection is
`\((2, -5)\)`.

To solve for the point of intersection between the lines
`\(y = -(3)/(2)x - 2\)` and
`\(y = -4x + 3\)` , we'll equate the two equations and solve for
`\(x\)`:

`\(-(3)/(2)x - 2 = -4x + 3\)`

First, let's eliminate the fractions by multiplying all terms by 2 to get rid of the denominator:

let's gather the
`\(x\)` terms on one side by adding
`\(8x\)` to both sides:

`\(5x - 4 = 6\)`

Now, isolate the
`\(x\)` term by adding 4 to both sides:

`\(5x = 10\)`

Finally, solve for
`\(x\)` by dividing both sides by 5:

`\(x = 2\)`

Now that we have
`\(x = 2\)` let's find the corresponding \(y\) value using one of the original equations. We'll use
`\(y = -(3)/(2)x - 2\)`:

`\(y = -(3)/(2)(2) - 2\)`

`\(y = -3 - 2\)`

`\(y = -5\)`

Therefore, the point of intersection occurs at
`\(x = 2\)` and
`\(y = -5\),` which gives us the coordinates of the intersection point as
`\((2, -5)\)`.

complete the question

"Two lines,
`\(y = -(3)/(2)x - 2\)` and
`\(y = -4x + 3\)`, intersect at a point. What are the coordinates of this point of intersection? Illustrate your answer graphically to show how you arrived at the solution."