Question

Input in standard form the equation of the given line.

The line that passes through (1, 5) and (-2, 3)

Answer 1

The slope t intercept equation of a line is y=mx + b

Use the slope formula to calculate the slope, m, of those two points first.

Once you find m, take any one of your two points. ex. (1,5) and sub it into the y=mx + b equation.

Let's say m = 5, then

y=mx + b

(5) = (5)(1) + b

5=5+b, solve for the y-intercept, b

b = 5 - 5 = 0

The equation of the line in slope y-intercept form is y=5x


To convert it into standard form, set the whole equation equal to 0

y=5x

-5x+y=0

multiply left and right side by -1 to remove the negative sign in the leading coefficient, -5.

-1(-5x+y)=-1(0)

5x-y=0 is the equation of the line in standard form.


The above is just a given example.

Answer 2

If you don't understand what I'm fixing to say just tell me so...

How do you put (1,5) and (-2,3) in a equation? Do you know how?

Answer 3

Actually, what he said is exactly how you do it, he just didn't do the problem for you.

Find the slope from two points \((x_1,y_1)\) and \((x_2,y_2)\):

\[m = \frac{y_2-y_1}{x_2-x_1}\]

Now use the point-slope formula:
\[y-y_1 = m(x-x_1)\]
Rearrange the result into whatever form you need. Standard form is \[Ax+By=C\]where \(A,B,C\) are integers, as I recall.

With my formula, what do you get for the slope with the two points in this question?