Q49. - Algebra 2

Question

Graph the line that satisfies each set of conditions.

Perpendicular to graph of $3x-2y=24$ intersects that graph at its 

x- intercept. 

Step-by-Step Solution

Answer

The required graph for the given equation with intercepts is,

Step 1. Determining the points which satisfy the equation 3 x - 2 y = 24 .

The equation $3x-2y=24$ in slope- intercept form is

$y=\left(\frac{3}{2}\right)x-12$

So, the slope is $\frac{3}{2}$ and $y$- intercept is $-12$

So, $(0,-12)$ satisfy the equation.

When $y=0$ in the given equation,

$\begin{array}{c}3x-2y=24\\ 3x=24\\ x=8\end{array}$

So, other point is $(8,0)$

Step 2. Determining the slope of the line that is perpendicular to given line

Slope of given line = $\frac{3}{2}$

Slope of line perpendicular to this line = $-\frac{2}{3}$.

Step 3. Determine the y -intercept.

The slope intercept form of line is 

$y=mx+c$

Since, $\begin{array}{c}m=-\frac{2}{3}\\ \text{or},y=-\frac{2}{3}x+c\end{array}$

Since, the line passes through $(8,0)$.

So, 

$\begin{array}{l}0=-\frac{2}{3}\times 8+c\\ c=-\frac{16}{3}\end{array}$

 Hence, the new equation formed is

 

$y=-\frac{2}{3}x-\frac{16}{3}$

Step 4. Concept of finding the points which satisfy the equations

Substitute $x=0$ in each equations and find the value of y and similarly put $y=0$ in each equations and find the value of x.

Step 5. Determining the point which satisfies the equations.

$(0,-\frac{16}{3})$ and $(-8,0)$ satisfy the equation $y=-\frac{2}{3}x-\frac{16}{3}$

Step 6. Plotting the graph.

The obtained graph from the given equation is,