Question

7. What do the following equations represent? 6x– 15y = 15y= 2/5x -1 are these theThe same lineParallel LinesPerpendicular LinesIntersecting lines that are not perpendicular

Answer 1

To determine if the lines of the equation system are parallel, perpendicular, equal, or not perpendicular, the first step is to write both equations in the slope-intercept form:

Equation 1

`6x-15y=15`

To write this equation in slope-intercept form, the first step is to pass the x-term 6x to the right side of the equation. For this, apply the opposite operation to both sides of it:

`\begin{gathered} 6x-6x-15y=-6x+15 \\ -15y=-6x+15 \end{gathered}`

The next step is to divide both sides by -15:

`\begin{gathered} -(15y)/(-15)=-(6x)/(-15)+(15)/(-15) \\ y=(2)/(5)x-1 \end{gathered}`

Equation 2:

This equation is already written on the slope-intercept form:

`y=(2)/(5)x-1`

As you can see both equations are equal, this means that this equation system has infinite solutions.