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:
[tex]slope=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}[/tex]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:
[tex]slope=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{300-0}{0-450}=\frac{300}{-450}=-\frac{2}{3}[/tex]And the intersection between the line and the y-axis is the point ( 0, 300 )
So, the value of b = 300
So,
[tex]\begin{gathered} m=-\frac{2}{3} \\ b=300 \end{gathered}[/tex]The equation of the line will be:
[tex]y=-\frac{2}{3}x+300[/tex]
