Question

write an equation of the line that passes through a pair of points (-5, -2), (4, 5)

Answer 1

To find the equation of a line knowing two points it passes through, we must first find the slope and then substitute the x and y values to figure out the y intercept. 

First thing is to find the slope using the formula m = Δy ÷ Δx
m = 5 - (-2) ÷ 4 - (-5)

Now we simplify 
m = 7 ÷ 9 

Our equation so far is y = 7/9x + b. Now we can substitute the values of x and y from a point to figure out the answer. The equation here uses the point (4,5)

5 = 7/9 · 4 + b

Get b on one side
5 - 28/9 = b

Simplify
b = 1 + 8/9

That makes the equation of the line y = 7/9x + (1 + 8/9)

Answer 2

Hello!

First of all we need to find the slope. We can use the equation below.

$\frac{ y_{2}- y_{1} }{ x_{2} - x_{1} }$

The ones and twos just represent a y or x value from one of the ordered pairs, so for example on ordered pair could represent the ones(note that the ones and twos can be switched and the slope will remain the same).

In our case we will have (-5,-2) be ($x_{1} ,y_{1}$) and (4,5) be ($x_{2} ,y_{2}$). We will plug this into the equation.

$\frac{5+2}{4+5} = \frac{7}{9}$

Therefore the slope of our line is 7/9.
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Now we need to find the y-intercept to have the equation for our line. We will put the slope and two points from the line into slope intercept form and solve for b (we will use (4,5)).

5=4(7/9)+b
5-b=3 1/9
5+(-b)=3 1/9
-b=-2 1/9
b=2 1/9

Now that we have our value for b we will put it in slope intercept form.

y=7/9x+(2 +1/9)

I hope this helps!