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2 years ago

What is the equation of a line that passes through (-6,2) and has a slope of ‘-(1)/(2)’?

Mathematics

1 answer:

alexandr1967 [171]2 years ago

8 0

Answer:

y= $-\frac{1}{2}$ x -1

Step-by-step explanation:

y=mx+c

y= $-\frac{1}{2}$ x +c

substitute (-6;2)

2= $-\frac{1}{2}$ (-6)+c

2=3+c

2-3=c

c=-1

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3 years ago

N Example 3, the points are(0,3500) and (5,1750). Write an equation that represents the distance y (in feet) remaining after x m

Cerrena [4.2K]

Answer:

<h2>The time needed is 10 months.</h2>

Step-by-step explanation:

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First, we use the formula below to find the slope of the line

$m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }=\frac{1750-3500}{5-0}=\frac{-1750}{5}=-350$

Which means the function is deacrasing with a ratio of 350 feet per month.

Now, we use the slope and one point to find the equation

$y-y_{1} =m(x-x_{1} )\\y-1750=-350(x-5)\\y=-350x+1750+1750\\y=-350x+3500$

This linear function shows that the situation started at the y-intecept (0, 3500), which means the month 0 had already 3500 feet. In other words, the total distance is 3500 feet. Now, the x-intercept will tell us the time needed to travel that distance.

$0=-350x+3500\\-3500=-350x\\x=\frac{-3500}{-350}\\ x=10$

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