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Zorluk: KolayLinear Equations in Two Variables

A student tracks the remaining battery percentage, yy, of a tablet after xx hours of use. The table below shows the battery percentage at three different times:

Time (xx, hours)Battery percentage (yy)
090
375
660

Which of the following equations represents the relationship between xx and yy?

  1. A
    y=−15x+90y = -15x + 90
  2. B
    y=−15x+90y = -\frac{1}{5}x + 90
  3. y=−5x+90y = -5x + 90Cevap
  4. D
    y=90x−5y = 90x - 5

Cevap

y = -5x + 90
The correct equation is y=−5x+90y = -5x + 90. According to the table, when time x=0x = 0, the battery percentage y=90y = 90, which indicates that the y-intercept of the line is 9090. The slope can be determined using any two points from the table, such as (0,90)(0, 90) and (3,75)(3, 75): slope=75−903−0=−153=−5\text{slope} = \frac{75 - 90}{3 - 0} = \frac{-15}{3} = -5. Writing this in slope-intercept form gives y=−5x+90y = -5x + 90.

Adım Adım Çözüm

1
Identify the y-intercept from the table.
The y-intercept bb is 9090.
When the time x=0x = 0 hours, the battery percentage y=90y = 90. This corresponds to the y-intercept of the linear equation.
2
Calculate the slope (rate of change) using two points from the table.
The slope mm is −5-5.
Using the points (0,90)(0, 90) and (3,75)(3, 75), the slope is calculated as the change in yy divided by the change in xx: m=75−903−0=−153=−5m = \frac{75 - 90}{3 - 0} = \frac{-15}{3} = -5.
3
Substitute the slope and y-intercept into the slope-intercept form equation.
y=−5x+90y = -5x + 90
Plugging m=−5m = -5 and b=90b = 90 into y=mx+by = mx + b yields the final equation.

Anahtar Kavram

Determining a linear equation in two variables from a table of values.
Tahmini Süre:1m 0s
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Konular

Linear Equations in Two Variables

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