Q32. - Algebra 2

Question

Graph the line that satisfies each set of conditions.

Passes through $\left(2,0\right)$, parallel to a line whose slope is 3       

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 $\left(2,0\right)$ and parallel to the a line whose slope is 3.

Parallel lines have same slope. This means slope of line is equivalent to slope of the line 3.

Therefore, the slope of the line is $m=3$.

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 $\left(2,0\right)$ move 3 units up (on y-axis) and 1 units right (on x-axis).

Therefore, the obtained ordered pair is $\left(3,3\right)$.

Step-3 – Graph the line

Plot the obtained ordered pairs $\left(2,0\right)$ and $\left(3,3\right)$ on Cartesian plane to obtain the graph of the line with slope $m=3$.