How to obtain the equation of a line knowing its graph
As you can see, the following graph corresponds to a straight line, the objective is to obtain the equation.
Note that the line intersects with the y-axis at b = 5, this means that the point (0.5) is on the graph of the equation.
Also we have additional information, if we remember the slope of the point of equations of the line y = mx + b, where b is the intersection of the line with the y-axis, so from the graph it follows that b = 5.
Note also in the graph, another point through which the line passes, that is (-5, -10).
With this information, we can find the slope of our line:
The slope formula is:
Corresponds to points (0.5) and (-5, -10) respectively.
Applying the slope formula we have:
m = (- 10-5) / (- 5-0) = (- 15) / (- 5) = 3
The slope of our line is 3, since it is positive that we conclude that the line is increasing (obviously it was seen in the graph, but we verified with the result).
With this result m = 3 and recalling that b = 5, we have the conditions to apply the slope point equation y = mx + b,
where we obtain that our equation is
Oh calculus! Made my life miserable while taking it. Haha.