Question

Use the graphing tool to graph the line. Use the given point when drawing the line.

Answer 1

We want to graph the equation of the line that contains the point (1 , 3), and has a slope of - 3/4.

Written in slope-intercept form, we have:

`y=-(3)/(4)x+b`

To find the 'b' coefficient, we can use our given point.

`3=-(3)/(4)\cdot1+b\Rightarrow b=(15)/(4)`

We have the following line equation

`y=-(3)/(4)x+(15)/(4)`

To draw the graph, we need two points of this line. We already have (1, 3), now, we just need another one that fits the line equation. An easy point to calculate is the x-intercept(y = 0).

`\begin{gathered} 0=-(3)/(4)x+(15)/(4)\Rightarrow(3)/(4)x=(15)/(4) \\ \Rightarrow3x=15\Rightarrow x=5 \end{gathered}`

With this, we know that the point (5, 0) also belongs to this line. To draw this line, we can just place the first dot at (1, 3), and the second dot at (5, 0).

The line equation have some different forms, one of them is the point-slope form. The point slope form is

`y-y_1=m(x-x_1)`

Where 'm' represents the slope of our line and (x1, y1) represents the coordinates of a given point of the line.

The given point in our line, is (1, 3), and the slope is -3/4. Writing in point slope form, we have:

`y-3=-(3)/(4)(x-1)`