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Mario compared the slope of the function graphed below to the slope of the linear function that has an x-intercept of 1 and a y-intercept of -2.


Find the slope of both lines. In the answer box give the slope of the steeper line.

Mario Compared The Slope Of The Function Graphed Below To The Slope Of The Linear Function That Has An Xintercept Of 1 And A Yintercept Of 2 Find The Slope Of B class=

Sagot :

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Answer:

The linear equation in the slope-intercept form will be:

[tex]y\:=\:\frac{2}{3}x+64[/tex]

Step-by-step explanation:

From the line graph, taking two points

  • (21, 78)
  • (27, 82)

Finding the slope between (21, 78) and (27, 82)

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

[tex]\left(x_1,\:y_1\right)=\left(21,\:78\right),\:\left(x_2,\:y_2\right)=\left(27,\:82\right)[/tex]

[tex]m=\frac{82-78}{27-21}[/tex]

[tex]m=\frac{2}{3}[/tex]

We know that the slope-intercept of the line equation is

[tex]y = mx+b[/tex]

where m is the slope and b is the y-intercept

substituting (21, 78) and m = 2/3 in the slope-intercept of the line

[tex]y = mx+b[/tex]

[tex]78=\frac{2}{3}\left(21\right)+b[/tex]

switch sides

[tex]\frac{2}{3}\left(21\right)+b=78[/tex]

[tex]14+b=78[/tex]

[tex]b=64[/tex]

substituting b = 64 and m = 2/3 in the slope-intercept of the line

[tex]y = mx+b[/tex]

[tex]y\:=\:\frac{2}{3}x+64[/tex]

Therefore, the linear equation in the slope-intercept form will be:

[tex]y\:=\:\frac{2}{3}x+64[/tex]

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