Write an exponential function in the form of y=ab^x passing through the points (0,6) and (2,96)
1 answer:
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<h3>Answer:</h3>
m= 15
b= 45
y= 15x +45
<h3>Concept:</h3><u>Overall equation</u>
The equation of a line in slope-intercept form is given by y= mx +b, where m is the slope and b is the y-intercept.
<u>Slope, m</u>
The slope is the measure of how steep the line is. It also defines how the y-axis changes with respect to the x-axis. The formula for finding slope is as shown below.
where is the first coordinate and
is the second coordinate
<u>y-intercept, b</u>
This is the y-value in which the line cuts through the y-axis (vertical axis).
<h3>Working:</h3><u>Slope, m</u>
Let's identify two pairs of coordinates on the line.
2 square units on the y-axis represent $30. Thus, 1 unit on the y-axis represents $15.
The 2 points are: (0, 45) and (5, 120)
Substitute the 2 points into the slope formula:
Slope
=
<em>= </em>
= 15
Thus, m= 15.
<u>y-intercept, b</u>
From the graph, the line cuts through the y-axis at y= 45.
Thus, b= 45.
<u>Overall equation</u>
Substitute m= 15 & b= 45 into y= mx +b:
∴ The equation of the line is y= 15x +45.
<h3>Additional:</h3>To learn more about slope-intercept form, do check out: brainly.com/question/26351470