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Type the equation that shows the pattern among this set of ordered pairs.
(0, -5), (1, 0), (2, 5), (3, 10)

Sagot :

TSOidn
First find the slope between any two points:

[tex]\sf Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

Where [tex]\sf (x_1,y_1),(x_2,y_2)[/tex] are the two points

So calculating the slope:

[tex]\sf Slope=\frac{5-0}{2-1}=\frac{5}{1}=5[/tex]

So the slope is [tex]\boxed{5}[/tex]

And our equation will be in the format of [tex]\sf y=mx+b[/tex]
where [tex]\sf m~ is~ the ~slope[/tex] and [tex]\sf b ~is~the~y-intercept[/tex]

So, now we have half of the equation:

[tex]\sf y= 5x+b[/tex]

Now to calculate b, we can plug in a point [tex]\sf (x,y)[/tex] and solve for b.

So

[tex]\sf y= 5x+b[/tex]

Lets use the point
[tex]\sf (1,0) which ~is~in~the~form ~of ~(x,y)[/tex]

So:
[tex]\sf 0=5(1)+b[/tex]

And then:
[tex]\sf b=-5[/tex]

So our final equation is [tex]\sf \boxed{y=5x-5}[/tex]
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