Question

A) What is the equation of the line that passes through the given pair points in slope-intercept form?

(2, 5.1) and (−1, −0.5)

B) What is the equation of the line that passes through the given pair points in slope-intercept form?
(−2, 3) and (3, −4)

Answer 1

A)

The slope-intercept form:

`y=mx+b`

m - slope

b - y-intercept

The formula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

We have the points (2, 5.1) and (-1, -0.5). Substitute:

`m=(-0.5-5.1)/(-1-2)=(-5.6)/(-3)=(5.6)/(3)=(56)/(30)=(28)/(15)`

Therefore we have:

`y=(28)/(15)x+b`

Put the coordinates of the point (-1, -0.5) ot the equation:

`-0.5=(28)/(15)(-1)+b`

`-0.5=-(28)/(15)+b` multiply both sides by 2

`-1=-(56)/(15)+2b` add
`(56)/(15)` to both sides

`(41)/(15)=2b` divide both sides by 2

`b=(41)/(30)`

Answer:
`\boxed{y=(28)/(15)x+(41)/(30)}`

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B)

We have the points (-2, 3) and (3, -4).

Calculate the slope:

`m=(-4-3)/(3-(-2))=(-7)/(5)=-(7)/(5)`

Therefore we have:

`y=-(7)/(5)x+b`

Put the coordinates of the point (-2, 3) to the equation of a line:

`3=-(7)/(5)(-2)+b`

`(15)/(5)=(14)/(5)+b` subtract
`(14)/(5)` from both sides

`(1)/(5)=b\to b=(1)/(5)`

Answer:
`\boxed{y=-(7)/(5)x+(1)/(5)}`