Question

In 30 words or fewer identify which form slope intercept or point slope would be better to use and why

Answer 1

The equation of the fourth line is;

`\begin{gathered} y-15=2(x-3)\text{ }\rightarrow\text{ point-slope form} \\ y=2x+9\text{ }\rightarrow\text{ Slope-intercept form} \end{gathered}`

Step-by-step explanation:

Given that the fourth line would also be parallel to the other three lines.

`\text{slope m = 2}`

And passes through the point;

`(x_1,y_1)=(3,15)`

Since, we have the value of the slope and we have a point on the fourth line;

Then we can use the point-slope form;

`y-y_{1_{}}=m(x-x_1)`

substituting the given values;

`\begin{gathered} y-15=2(x-3) \\ y-15=2x-6 \\ y=2x-6+15 \\ y=2x+9 \end{gathered}`

Therefore, the equation of the fourth line is;

`\begin{gathered} y-15=2(x-3)\text{ }\rightarrow\text{ point-slope form} \\ y=2x+9\text{ }\rightarrow\text{ Slope-intercept form} \end{gathered}`

To derive the equation of the fourth line, the best and easiest equation to use is the point-slope form. because we were given the slope and a point on the slope.