allybelle2018
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A scatter plot of data comparing the number of years since Holbrook High
School introduced a math club and the number of students participating
contains the ordered pairs (3, 19) and (8, 42). Which is the slope-intercept
form of an equation for the line of fit containing those points?

Respuesta :

lucic

[tex]y=\frac{23}{5} x+\frac{26}{5}[/tex]

Step-by-step explanation:

Slope intercept form of an equation is written as;

y=mx+b where m is the slope of the line and b is the y-intercept

Given points (3,19) and (8,42) find m as;

m=Δy/Δx

Δy=42-19=23

Δx=8-3=5

m=23/5

Finding the equation of the line where m=23/5, point (3,19) and (x,y)

m=Δy/Δx

23/5=y-19/x-3

cross product

23(x-3) = 5(y-19)

23x-69=5y-95

23x=5y-95+69

23x=5y-26

23x+26=5y

23x/5 +26/5 =5y/5

23/5 x +26/5 =y

⇒⇒   y=23/5x +26/5

Learn More

Slope-intercept form of an equation :https://brainly.com/question/12005129

Keywords :scatter plot, data, years, line of fit, points

#LearnwithBrainly

Cricetus

The slope-intercept  form of an equation will be "y = 4.6x + 52".

Given:

Points,

  • [tex](x_1, y_1) =(3, 19)[/tex]
  • [tex](x_2,y_2) = (8, 42)[/tex]

As we know,

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

               [tex]= \frac{42-19}{8-3}[/tex]

               [tex]= \frac{23}{5}[/tex]

The equation of line,

→ [tex]y = mx+b[/tex]

  [tex]y = \frac{23}{5}x+b[/tex]

It passes through (3, 19), the

→ [tex]19 = \frac{23}{5}\times 3+b[/tex]

    [tex]b = 19-\frac{69}{5}[/tex]

    [tex]b = \frac{26}{5}[/tex]

hence,

The slope-intercept form equation:

→ [tex]y = \frac{23}{5} x+\frac{26}{5}[/tex]

  [tex]y = 4.6x+52[/tex]

Thus the above response is appropriate.

Learn more about slope here:

https://brainly.com/question/15053069

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