What is slope-intercept form of a line that passes through points (2,11) and (4,17)?

Mathematics

1 answer:

kramer2 years ago

6 0

Answer:

y = 3x + 5

Step-by-step explanation:

Okay, so first we do the equation for rise over run which is y2 - y1/ x2 - x1

so plug the numbers 11 - 17/ 4 - 2 getting the slope -3, now since we found the slope we need to find the intercept form, what you have to do now is plug in a coordinate from the x value and y value one of the pairs essentially so,

y = 3x + b, I chose your first pair

11 = 3 x 2 + b

equals to,

11 = 6 + b

now we want b, by itself.

5 = b

so the total intercept form answer is

y = 3x + 5

I will check over it,

11 = 3 x 2 + 5

11 = 11

I hope this helped!

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Find the distance points p (3,6) and q (7,3) to the nearest tenth?

Vladimir79 [104]

<h3>Answer: 5</h3>

=========================================================

One method is to plot the points P(3,6) and Q(7,3) on the same xy grid. Plot a third point R at (3,3). See the diagram below.

A right triangle forms in which we can find the legs PR = 3 and RQ = 4. The hypotenuse is found through the pythagorean theorem.

a^2+b^2=c^2

3^2+4^2 = c^2

9+16 = c^2

c^2 = 25

c = sqrt(25)

c = 5

This is the length of PQ

-----------------------------------

Or you can use the distance formula which is effectively using the pythagorean theorem just in a slightly different format (though it may not be obvious).

$d = \text{Distance from P to Q}\\\\d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{(3-7)^2+(6-3)^2}\\\\d = \sqrt{(-4)^2+(3)^2}\\\\d = \sqrt{16+9}\\\\d = \sqrt{25}\\\\d = 5\\\\$