Question

A line is drawn so that it passes through the points (-3, -1) and (4, 2).

a. What is the slope of the line?

b. Using the point (4, 2) and the slope found above, write the equation of the line in point-slope form.

Note: you can write fractions like this: (2/5)

Answer 1

m=3/7, y=3/7x+2/7

Step-by-step explanation:

The formula for the slope is:

y₂-y₁

m= --------

x₂-x₁

Our first coordinate pair is:

(-3,-1) . -3 is our x₁ and -1 is our y₁ .

Our second coordinate pair is:

(4,2) . 4 is our x₂ and 2 y₂ .

We can substitute our numbers into the original equation and simplify:

2-(-1) 3

m= ------- = -----

4-(-3) 7

Ok, now that we know our slope, we can find the equation...

Substitute in your slope and any coordinate pair into y=mx+b: (I'll be using (4,2) as my coordinate pair.)

2=(3/7)(4)+b

Then solve:

(3/7) x (4/1) = 12/7

2=12/7+b

2/1-12/7=b

2/7=b

Now that we have our slope and our y-intercept, we can FINALLY make an equation:

y=3/7x+2/7

That's a lot of work, but I hope I helped!

:)

Answer 2

(A)
`\boxed{\bold{y=(3)/(7)x+(2)/(7)}}`

(B)
`\boxed{\bold{2 \ = \ (3)/(7) * \ 4 \ + \ (2)/(7)  }}`

Step-by-step explanation:

(A) Slope: y = mx + b

m = 3/7

b = 2/7

Slope =
`\bold{(y_2-y_1)/(x_2-x_1)}`

`\bold{\left(x_1,\:y_1\right)=\left(-3,\:-1\right),\:\left(x_2,\:y_2\right)=\left(4,\:2\right)}`

M =
`\bold{(2-\left(-1\right))/(4-\left(-3\right)): \ (3)/(7) }`

Y intercept

`\bold{y=(3)/(7)x+b}`

Plug in
`\bold{\left(-3,\:-1\right)\mathrm{:\:}\quad \:x=-3,\:y=-1}`

`\bold{-1=(3)/(7)\left(-3\right)+b}`

Isolate B

`\bold{-1=(3)/(7)\left(-3\right)+b}`

b =
`\bold{(2)/(7) }`

(B) 4 = x, 2 = y

2 = 3/7 * 4 + 2/7