Question

What is the equation for a line that passes through the points (5,-3) and (-10,15)?

Answer 1

Answer:

$6x + 5y = 15\:or\:y = -1\frac{1}{5}x + 3$

Step-by-step explanation:

First find the rate of change [slope]:

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

$\frac{3 + 15}{-5 - 10} = -\frac{18}{15} = -1\frac{1}{5}$

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:

15 = −1⅕[−10] + b

12

$3 = b \\ \\ y = -1\frac{1}{5}x + 3$

If you want it in Standard Form:

y = −1⅕x + 3

+1⅕x + 1⅕x

______________

$1\frac{1}{5}x + y = 3$[We do not want fractions in our Standard Equation, so multiply by the denominator to get rid of it.]

5[1⅕x + y = 3]

$6x + 5y = 15$

_______________________________________________

−3 = −1⅕[5] + b

−6

$3 = b \\ \\ y = -1⅕x + 3$

y = −1⅕x + 3

+1⅕x + 1⅕x

______________

$1⅕x + y = 3$[We do not want fractions in our Standard Equation, so multiply by the denominator to get rid of it.]

5[1⅕x + y = 3]

$6x + 5y = 15$

** 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.