Q23. - Algebra 2

Question

Graph the line passing through the given point with the given slope

$\text{ (1,-3), 2}$

Step-by-Step Solution

Answer

The graph of the line passing through the point $(1,-3)$ with the slope $2$ is

Step-1 – Apply the concept of slope of a line

The slope of a line is the ratio of the change in the y-coordinates to the change in the x- coordinates.

Symbolically, the slope m of the line passing through the points $\left(x_1,y_1\right)\text{ and }\left(x_2,y_2\right)$ is given by $m=\frac{y_2-y_1}{x_2-x_1}$ where $x_1\ne x_2$.

Step-2 – Plot the given ordered pair

The given ordered pair is $\left(1,-3\right)$

Hence plot the point in the graph such that the point is 1 unit in the $x-$axis and 3 units in the negative y-axis.

Therefore, the point $\left(1,-3\right)$ in the graph is as shown below:

Step-3 – Find a new point using the slope

Since the slope is 2, it can also be written as $\frac{2}{1}$(since $\frac{a}{1}=a$)

Hence according to the given slope, go up 2 units and right 1. Now, plot the new point at $\left(2, -1\right)$.

Therefore the new point in the graph is given as below:

Step-4 – Graph the line

Draw a line containing the points $\left(1,-3\right)\text{ and }\left(2,-1\right)$. Therefore the graph is