the equation for The line that passes through (-3, 5) and (-2, -6)

Question

Can you help me with this question?

 

The equation for the line that passes through (-3,5) and (-2,-6)

Answer 1

Hi Anthony;

You stated "the equation".  I am assuming that your instructor wants standard equation.

(-3, 5) and (-2, -6)

The first thing we need to do is establish the slope of the line.  Slope is defined as the change-of-y divided by the change-of-x...

(y-y₁)/(x-x₁)

(5--6)/(-3--2)

(5+6)/(-3+2)

11/-1

-11

The standard format of an equation is...

Ax+By=C, neither A nor B equal zero and A is greater than zero.

slope=-A/B

slope=-(-11/1)

slope=11/1

11x+1y=C

11x+y=C

Let's plug-in one point to establish C...

(-3, 5) and (-2, -6)

11x+y=C

[11(-3)]+5=C

-33+5=-28

Let's verify with the other point...

[11(-2)]+-6=C

-22-6=c

-28=c

11x+y=-28

Answer 2

Hi Anthony!

 

To write an equation for a line given two points, you can:

1. Find the slope.

2. Use the slope and a given point to write the equation in point-slope form.

3. Solve for slope-intercept form if that is necessary.

 

Here's how you do it for this problem:

1. Find the slope using slope formula ("rise over run"):

m = rise/run = (y₂ - y₁)/(x₂ - x₁)

 

For this problem:

(x₁, y₁) = (-3,5)

(x₂, y₂) = (-2,-6)

 

Plug those values into slope formula:

m = (-6 - 5)/(-2 - (-3))

Watch your signs and simplify:

m = (-11)/(1) = -11

So, your slope is -11.

 

2. Now, you can write the line equation in point-slope form, which looks like this:

y - y₁ = m(x - x₁)

 

Plug in the slope you found, and one of the given points. I'll use (-3,5), but you can use either.

 

y - 5 = -11(x - (-3))

y - 5 = -11(x + 3)

That is the equation in point-slope form.

 

3. You can then simplify to slope-intercept form, y = mx + b.

Use the point-slope form, and solve for y ("get y alone on one side of the equals sign"):

 

y - 5 = -11(x + 3)

y - 5 = -11x - 33

y = -11x - 33 + 5

y = -11x - 28

 

In slope-intercept form, your answer is:

y = -11x - 28

 

Hope this helps!