AFirst, use the given points to calculate the slope.
Then, identify the y-intercept.
BRecall the meaning of x and y.
AGraph:
Equation: y=- x +65
BSee solution.
Practice makes perfect
Consider that an unmanned aerial vehicle (UAV) is used for surveillance. We are given a table that shows the height y in thousands of feet of the UAV x minutes after it begins to descend from cruising altitude. Be aware that in this case the rate of descent doubles.
Minutes, x
Height, y
0
65
10
55
20
45
We want to write a linear function that relates y to x. To do so, remember that functions written in slope-intercept form follow a specific format.
y= mx+ b
In this form, m is the slope and b is the y-intercept. We need to identify these values using the given table. Let's start by substituting the points (0,65) and (10,55), into the slope formula and calculating m.
The y-intercept occurs when x=0. From the table we can see that when x=0 the value of y is 65.
Minutes, x
Height, y
0
65
10
55
20
45
Then, the y-intercept is 65. Now we can write a linear function that relates y to x.
y= - 1x+ 65 → y= - x+65
Finally, we will plot the points in the table and draw a line through the points.
Since x represents the minutes and y the height in thousands of feet, the slope indicates that the height decreases 1000 feet per minute. The y-intercept represents that the descent begins at a cruising altitude of 65 000 feet.
