Answer:
[tex]-\frac{3}{4}[/tex]
Step-by-step explanation:
the equation for finding the slope of a line when given two points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], aka the change in y over the change in x.
pick one of your coordinate pairs to be [tex]y_2\\[/tex] and [tex]x_2[/tex]. it doesn't matter which coordinate pair you choose as long as you keep them as [tex]y_2\\[/tex] and [tex]x_2[/tex]. the remaining coordinate pair will be [tex]y_1[/tex] and [tex]x_1[/tex].
for this example, i'll use (2, 10) for [tex]y_2\\[/tex] and [tex]x_2[/tex] and (6, 7) for [tex]y_1[/tex] and [tex]x_1[/tex].
**before i begin, i just want to note that you can do these next four steps in any order that you want. i personally prefer to plug in my y-values first and then my x-values, but you can choose to instead plug in the values of each coordinate pair (like starting by plugging in the coordinate pair (2, 10) with 10 for [tex]y_2\\[/tex] and 2 for [tex]x_2[/tex]). it's up to you. i'm going to explain the steps by plugging in my y-values first and then my x-values because that's the way i normally do it.
first, start by plugging in the y-value from the coordinate pair of your choosing in for [tex]y_2\\[/tex]. since i chose (2, 10) for [tex]y_2\\[/tex] and [tex]x_2[/tex], i'll plug in 10 for [tex]y_2\\[/tex].
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex] ⇒ [tex]\frac{10-y_1}{x_2-x_1}[/tex]
then plug in the remaining coordinate pair's y-value in for [tex]y_1[/tex]. since the coordinate pair that's left is (6, 7), i will plug in 7 for [tex]y_1[/tex].
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex] ⇒ [tex]\frac{10-7}{x_2-x_1}[/tex]
now i'm going to plug in the x-values. i chose (2, 10) to plug in for [tex]y_2\\[/tex] and [tex]x_2[/tex], so now i'll plug in 2 for [tex]x_2[/tex].
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex] ⇒ [tex]\frac{10-7}{2-x_1}[/tex]
and all that's left to plug in is the x-value from (6, 7), so i will plug that in for [tex]x_1[/tex].
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex] ⇒ [tex]\frac{10-7}{2-6}[/tex]
after plugging in all the values, you have [tex]\frac{10-7}{2-6}[/tex].
subtract 10 - 7 as well as 2 - 6.
[tex]\frac{10-7}{2-6}[/tex] ⇒ [tex]\frac{3}{-4}[/tex]
[tex]\frac{3}{-4}[/tex] cannot be simplified, therefore the slope of the line is [tex]\frac{3}{-4}[/tex] or [tex]-\frac{3}{4}[/tex].
i hope this helps! have a lovely day <3
