Question

2c3y = 10 In the ry-plane, the graph of which of the following equations is perpendicular to the graph of the equation above?

Answer 1

The equation of the line in Slope-Intercept form is the following:

`y=mx+b`

Where "m" is the slope of the line and "b" is the y-intercept.

In this case, you have the following equation of a line:

`2x+3y=10`

To write it in Slope-Intercept form, you must solve for "y":

`\begin{gathered} 2x+3y=10 \\ 3y=-2x+10 \\ y=-(2)/(3)x+(10)/(3) \end{gathered}`

So you can see that its slope is:

`m_1=-(2)/(3)`

The slopes of perpendicular lines are opposite reciprocals, then you can determine that the slope of the other line is:

`m_2=(3)/(2)`

You can see in the picture that the only equation that has this slope is the one shown