Question

Given the equation y =2x-1 and the points (1,1), (3,5), (7,13) show that the slope is the same between these pairs.​

Answer 1

Proved!

Explanation:

In this problem, we have the following linear equation:

$y=2x-1$

And three points:

$(1,1) \\ \\  (3,5) \\ \\  (7,13)$

The equation is written in Slope-intercept form:

$y=mx+b \\ \\ \\ Where: \\ \\m:Slope \\ \\ b:y-intercept$

So the slope of our equation is:

$m=2$

For the points, the slope can be found as:

$m=\frac{Change \ in \ y}{Change \ in \ x}$

There will be 3 combinations of points for which you have to prove that slope is equal:

a) 1st and 2nd point:

$(1,1) \ and \ (3,5) \\ \\ m=\frac{5-1}{3-1}=\frac{4}{2}=2$

b) 2nd and 3rd point

$(3,5) \ and \ (7,13) \\ \\ m=\frac{13-5}{7-3}=\frac{8}{4}=2$

c) 3rd and 1st point

$(1,1) \ and \ (7,13) \\ \\ m=\frac{13-1}{7-1}=\frac{12}{6}=2$

As you can see, both slopes are the same.

PROVED!

Learn more:

System of linear equations: https://brainly.com/question/13799715

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