Q47. - Algebra 2

Question

Graph the line that satisfies each set of conditions.

47. Passes through $\left(2,-1\right)$ parallel to graph of $2x+3y=6.$

Step-by-Step Solution

Answer

The graph of the required line is:

Step 1- Given information

A point $(2,-1)$ and an equation $2x+3y=6$.

Step 2- Calculation

From given information,

A point $(2,-1)$ and $2x+3y=6$

Here, x-intercept is:

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

y- intercept is:

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

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

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

We get a new point $\left(5,-3\right)$.

Now we draw the line which is contained both the points $(2,-1)$ and $\left(5,-3\right)$.

Step 3- Graph of the line

The graph of the required line is: