Q33. - Algebra 2

Question

Graph the line that satisfies each set of conditions.

 

Passes through $\left(-1,-2\right)$, perpendicular to a line whose slope is $\frac{1}{2}$                                   

Step-by-Step Solution

Answer

The graph of the line is provided below.

Step-1 – Apply the concept of slope

The slope of the line passing through the points $\left(x_1,y_1\right)\text{ and }\left(x_2,y_2\right)$ is expressed below.

$m=\frac{y_2-y_1}{x_2-x_1}$

Step-2 –Compute the intercept

The y-intercept of a graph is when the x-coordinate is 0. The point where the graph of the equation cuts the y-axis. 

It is provided that line passes through the point $\left(-1,-2\right)$ and perpendicular to a line whose slope is $\frac{1}{2}$.

Product of slopes of perpendicular lines is $-1$. This means slope of line is $-1$ divided by slope of the line $\frac{1}{2}$.

Therefore, the slope of the line is evaluated below.

$\begin{array}{c}m=\frac{-1}{\frac{1}{2}}\\ m=-2\end{array}$

To obtain the other ordered pair through which the line passes interpret the slope. The slope is positive this means the line rises to the right.

Now, from the ordered pair $\left(-1,-2\right)$ move 2 units up (on y-axis) and 1 units left (on x-axis).

Therefore, the obtained ordered pair is $\left(-2,0\right)$.

Step-3 – Graph the line

Plot the obtained ordered pairs $\left(-1,-2\right)$ and $\left(-2,0\right)$ on Cartesian plane to obtain the graph of the line with slope $m=-2$.