Question

Graph the line with slope -2 passing through the point (3,5)

Answer 1

To graph the line, you need to know at least two points of it.

Knowing its slope and one point you can determine the equation of the line by using the point-slope form:

`y-y_1=m(x-x_1_{})`

Where

m is the slope of the line

(x₁,y₁) are the coordinates of one point of the line

For m=-2 and (x₁,y₁)=(3,5) the equation of the line is:

`y-5=-2(x-3)`

Next, replace the equation for any value of x and solve for y, for example, use x=2

`y-5=-2(2-3)`

-Solve the difference within the parentheses then the multiplication

`\begin{gathered} y-5=-2(-1) \\ y-5=2 \end{gathered}`

-Add 5 to both sides of the equation

`\begin{gathered} y-5+5=2+5 \\ y=7 \end{gathered}`

The coordinates for the second point are (2,7)

Plot both points and link them with a line