Question

What is an equation of the line that passes through the points (1,3) and (8,5)

Answer 1

Answer:

$2x - 7y = -19\:or\:y = \frac{2}{7}x + 2\frac{5}{7}$

Step-by-step explanation:

First, find the rate of change [slope]:

$\frac{-y_1 + y_2}{-x_1 + x_2} = m$

$\frac{-3 + 5}{-1 + 8} = \frac{2}{7}$

Then plug these coordinates into the Slope-Intercept Formula instead of the Point-Slope Formula because you get it done much swiftly. It does not matter which ordered pair you choose:

5 = 2⁄7[8] + b

2 2⁄7

$2\frac{5}{7} = b \\ \\ y = \frac{2}{7}x + 2\frac{5}{7}$

If you want it in Standard Form:

y = 2⁄7x + 2 5⁄7

- 2⁄7x - 2⁄7x

________________

−2⁄7x + y = 2 5⁄7 [We do not want fractions in our Standard Equation, so multiply by the denominator to get rid of it.]

−7[−2⁄7x + y = 2 5⁄7]

$2x - 7y = -19$

__________________________________________________________

3 = 2⁄7 + b

$2\frac{5}{7} = b \\ \\ y = \frac{2}{7}x + 2\frac{5}{7}$

y = 2⁄7x + 2 5⁄7

- 2⁄7x - 2⁄7x

_______________

−2⁄7x + y = 2 5⁄7 [We do not want fractions in our Standard Equation, so multiply by the denominator to get rid of it.]

−7[−2⁄7x + y = 2 5⁄7]

$2x - 7y = -19$

** You see? I told you it did not matter which ordered pair you choose because you will always get the exact same result.

I am joyous to assist you anytime.