Write the equation of the linear function that goes through the points (5,-1) and (-5,9)

Question

I don't understand how to make the equation for this problem help?

Answer 1

there are two ways to go about finding the equation of the line. You can use point slope form or the y intercept form. Either are valid it just depends on what you're looking for. 

 

For both the first atep is to find the slope of the line.

To find the slope you use the following equation:

m = (y1-y2)/(x1-x2)

 

(5, -1) = (x1,y1)

(-5, 9) = (x2,y2)

 

it does not matter which point you designate 1 or 2 as long as you are consistent. Now we find the slope.

 

m= (-1 - 9)/(5 - (-5) )

m = -10 / 10

m = -1

 

 

Point Slope Form is the easier way to find the equation.

 

point slope form is:

 

y - y1 = m(x - x1)

 

All you need for the point slope form is the slope, which we found, and a point on the line, which we also have.

 

now you just substitute the slope and one of the points into the equation.

 

(-5, 9)

y - 9 = -1(x - (-5))

y - 9 = -1(x + 5)

 

or 

(5, -1)

y - (-1) = -1(x - 5)

y + 1 = -1(x -5)

 

For the y intercept form or standard form you need the slope of the line and the y intercept. 

 

Standard form: y = mx + b

 

we already found the slope, m= -1

 

now we just need the y intercept (b).

 

To find b you can plug inthe slope and one point into the equation and solve for b.

 

I'm using the point (-5,9)

y= mx+ b

9 = (-1)(-5) + b

9 = 5 + b

4 = b

 

Now that we have the slope, m, and the y intercept, b, we use those to form the equation of the line.

 

y = mx+ b

y = -1x + 4

y = -x + 4

 

If you take the point slope forms that we found above and solve for y they will match the standard form equation.

Answer 2

To solve this, the best equation would be to use the point-slope format:

y - y₁ = m(x - x₁)

 

First we need the slope, which is rise over run, or (y₂ - y₁)/(x₂ - x₁)

m = (9 - (-1)) / (-5 - 5)

m = 10 / -10

m = -1

 

So now we have the slope, we just use a point:

y - -1 = -1(x - 5)

y + 1 = -(x - 5)

 

We can keep it as is, or we can clean it up and make it the more familiar slope-intercept formula:

y + 1 = -x + 5

y = -x + 4

 

We can check our answer by plugging in our two points into our slope-intercept form:

-1 = -5 + 4

-1 = -1

 

9 = -(-5) + 4

9 = 5 + 4

9 = 9