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Which function has the greatest rate of change? A) y = 3x - 4 B) 4y - 8x = 1 C) a line passing through points (2,6) and (3,10) D) a line passing through points (5,−2) and (6, 4)

Respuesta :

apologiabiology
greatest rate of change is the slope

the slope between the oints (x1,y1) and (x2,y2) is
(y2-y1)/(x2-x1)
and
y=mx+b
m=slope
and
ax+by=c, -a/b is slope


A. y=3x-4, slope is 3
B. -8x+4y=1, slope=-(-8)/4=8/4=2
C. (2,6) dn (3,10), (10-6)/(3-2)=4/1=4
D. (5,-2) and (6,4), (4-(-2))/(6-5)=(4+2)/(1)=6/1=6


A. 3
B. 2
C.4
D.6

6>4>3>2

D has greatest slope (line passing throuh (5,-2) and (6,4))

A line passing through points (5,−2) and (6, 4) has the greatest rate of change which is 6.

We have to determine, which function has the greatest rate of change.

  • The greatest rate of change is the slope is determined by the slope point form given below.

The slope of the line  [tex]y = mx+c[/tex] is defined as a slope that is equal to m.

The slope of the line y = 3x - 4,  

The slope of the line m is 3.

And The slope of the line -8x + 4y = 1,

Then, The slope of the line m = -(-8)/4 =8/4 =2.

  • The slope of the point [tex](x_1, x_2)[/tex] and [tex](y_1, y_2)[/tex] is determined by the formula given below,

[tex]m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]

And The slope of the line passes through points (2,6) and (3,10) is,

[tex]m = \dfrac{10-6}{3-2}\\\\m = \dfrac{4}{1}\\\\m = 4[/tex]

And The slope of the line passes through points (5,−2) and (6, 4) is,

[tex]m = \dfrac{4-(-2)}{6-5}\\\\m = \dfrac{6}{1}\\\\m = 6[/tex]

Hence, The slope of the function is 6>4>3>2 and the greatest rate of change ) a line passing through points (5,−2) and (6, 4) is 6.

To know more about Slope click the link given below.

https://brainly.com/question/19214360