Q11. - Algebra 2

Question

Graph the line that satisfies each set of conditions.

Passes through $\left(-1,5\right)$ perpendicular to graph of $5x-3y-3=0.$

Step-by-Step Solution

Answer

The graph of the required line is:

Step 1- Given information

A point $(-1,5)$ and an equation $5x-3y-3=0$.

Step 2- Calculation

From given information,

A point $(-1,5)$ and $5x-3y-3=0$

Here, x-intercept is:

$\begin{array}{l}5x-3\times 0=3\\ \Rightarrow 5x=3\\ \Rightarrow x=\frac{3}{5}\end{array}$

y- intercept is:

$\begin{array}{l}5\times 0-3y=3\\ \Rightarrow -3y=3\\ \Rightarrow y=-1\end{array}$

Therefore, the line goes to $1$ units up and $\frac{3}{5}$ units right then.

So, the slope of the line is $\frac{5}{3}$.

The slope of the perpendicular line is the opposite reciprocal of $\frac{5}{3}$ is $-\frac{3}{5}.$

Now, start at $(-1,5)$ and go 3 units below and 5 units right then,

We get a new point $\left(4,2\right)$.

Now we draw the line which is contained both the points $(-1,5)$ and $\left(4,2\right)$.

Step 3- Graph of the line

The graph of the required line is: