Writing An Equation From A Graph
WRITING AN EQUATION FROM A GRAPH
We can use information presented in a graph to write an equation in slope-intercept form.
Example 1 :
A video club charges a one-time membership fee plus a rental fee for each DVD borrowed. Use the graph to write an equation in slope-intercept form to represent the amount spent, y, on x DVD rentals.
Solution :
Step 1 :
Choose two points on the graph, (x1 , y1 ) and (x 2 , y2 ), to find the slope.
Find the ratio between change in y-values and change in x-vales.
m = (y2 - y1 ) / ( x2 - x1 )
Substitute :
(x1, y1) = (0, 8)
(x2 , y2) = (8, 18)
Then,
m = (18 - 8 ) / (8 - 0 )
m = 10 / 8
m = 1.25
Step 2 :
Read the y-intercept from the graph. That is, the point at which the line cuts y-axis.
The y-intercept is 8.
b = 8
Step 3 :
Let us use slope (m) and y-intercept (b) values to write an equation in slope-intercept form.
y = mx + b ( Slope-intercept form)
Substitute m = 1.25 and b = 8.
y = 1.25x + 8
Example 2 :
The cash register subtracts $2.50 from a $25 Coffee Café gift card for every medium coffee the customer buys. Use the graph to write an equation in slope-intercept form to represent this situation.
Solution :
Step 1 :
Choose two points on the graph, (x1 , y1) and (x 2 , y2 ), to find the slope.
Find the ratio between change in y-values and change in x-values.
m = (y2 - y1 ) / ( x2 - x1 )
Substitute :
(x1, y1) = (0, 25)
(x2 , y2) = (10, 0)
Then,
m = (0 - 25 ) / (10 - 0 )
m = -25 / 10
m = -2.5
Step 2 :
Read the y-intercept from the graph. That is, the point at which the line cuts y-axis.
The y-intercept is 25.
Step 3 :
Let us use slope (m) and y-intercept (b) values to write an equation in slope-intercept form.
y = -2.5x + 25 ( Slope-intercept form)
Substitute m = -2.5 and b = 25.
y = -2.5x + 25
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Writing An Equation From A Graph
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