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

Answer:

(A) $\boxed{\bold{y=\frac{3}{7}x+\frac{2}{7}}}$

(B) $\boxed{\bold{2 \ = \ \frac{3}{7} * \ 4 \ + \ \frac{2}{7}  }}$

Explanation:

(A) Slope: y = mx + b

m = 3/7

b = 2/7

Slope = $\bold{\frac{y_2-y_1}{x_2-x_1}}$

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

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

Y intercept

$\bold{y=\frac{3}{7}x+b}$

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

$\bold{-1=\frac{3}{7}\left(-3\right)+b}$

Isolate B

$\bold{-1=\frac{3}{7}\left(-3\right)+b}$

b = $\bold{\frac{2}{7} }$

(B) 4 = x, 2 = y

2 = 3/7 * 4 + 2/7

Answer 2

Answer:

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!

                                                     :)