Q10. - Algebra 2

Question

Graph the line that satisfies each set of conditions.

10. Passes through $\left(4,-2\right)$ perpendicular to graph of $3x-2y=6.$

Step-by-Step Solution

Answer

The graph of the required line is:

Step 1- Given information

A point $(4,-2)$ and an equation $3x-2y=6$.

Step 2- Calculation

From given information,

A point $(4,-2)$ and $3x-2y=6$

Here, x-intercept is:

$\begin{array}{l}3x-2\times 0=6\\ \Rightarrow 3x=6\\ \Rightarrow x=2\end{array}$

y- intercept is:

$\begin{array}{l}3\times 0-2y=6\\ \Rightarrow -2y=6\\ \Rightarrow y=-3\end{array}$

Therefore, the line goes to $3$ units up and 2 units right then.

So, the slope of the line is $\frac{3}{2}$.

The slope of the perpendicular line is the opposite reciprocal of $\frac{3}{2}$ is $-\frac{2}{3}.$

Now, start at $(4,-2)$ and go 2 units below and 3 units right then,

We get a new point $\left(7,-4\right)$.

Now we draw the line which is contained both the points $(4,-2)$ and $\left(7,-4\right)$.

Step 3- Graph of the line

The graph of the required line is: