Question

I need to know how to write the equation of the line that represents a graph

Answer 1

The question is: how to write the equation of the line that represents a graph?

The general equation of the line has the form: y = m * x + b

Where m is the slope of the line and (b) is the y-intercept

So, from the graph of the line choose 2 points lying on the line:

( x1, y1 ) and ( x2, y2 ) and calculate the slope using the formula:

`slope=(rise)/(run)=(y_2-y_1)/(x_2-x_1)`

So, we have found the value of m

To find the value of b, find the point that intersects with the y-axis

So, b = y-coordinate

Finally, substitute with the value of (m) and (b) in the general form of the line.

Let us apply that to the following line:

As shown, the line passes through the points ( 450, 0 ) and ( 0, 300 )

So, the slope of the line will be:

`slope=(rise)/(run)=(y_2-y_1)/(x_2-x_1)=(300-0)/(0-450)=(300)/(-450)=-(2)/(3)`

And the intersection between the line and the y-axis is the point ( 0, 300 )

So, the value of b = 300

So,

`\begin{gathered} m=-(2)/(3) \\ b=300 \end{gathered}`

The equation of the line will be:

`y=-(2)/(3)x+300`