Question

I need to find out the point where the two lines intersect-3x+5 & 1.5x-4

Answer 1

both lines will intersect at x = 2

Step-by-step explanation:

Given:

-3x + 5 and 1.5x - 4

To get the point of intersection, we can plot the graphs of both expressions or we can equate both equations

Equating both expressions:

-3x + 5 = 1.5x - 4

`\begin{gathered} \text{collect like terms by adding 3x to both sides:} \\ -3x\text{ + 3x + 5 =1.5x +3x - 4} \\ 5\text{ = 4.5x - 4} \\ \\ \text{Add 4 to both sides:} \\ 5\text{ + 4 = 4.5x - 4 + 4} \\ 9\text{ = 4.5x} \end{gathered}`
`\begin{gathered} \text{divide both sides by 4.5:} \\ (9)/(4.5)\text{ = }(4.5x)/(4.5) \\ 2\text{ = x} \end{gathered}`

Point of intersection is when both lines have same value

Hence, both lines will intersect at x = 2