Examine the linear graph to find the slope , y-intercept, and write the equation for this linear relationship ​

Answer:

The slope of the line is: [tex]m=-\frac{1}{2}[/tex]

The y-intercept b = 3

The slope-intercept equation of the line is:  [tex]y\:=\:-\frac{1}{3}x+3[/tex]

Step-by-step explanation:

Taking two points from the given graph

(0, 3) and (6, 0)

Determining the slope m

The slope between (0, 3) and (6, 0) using the formula

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

where m is the slope between (x₁, y₁) and (x₂, y₂)

In our case,

now substitute (x₁, y₁) = (0, 3) and (x₂, y₂) = (6, 0) in the slope formula

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

[tex]m=\frac{0-3}{6-0}[/tex]

[tex]m=-\frac{3}{6}[/tex]

[tex]m=-\frac{1}{2}[/tex]

Thus, the slope of the line is: [tex]m=-\frac{1}{2}[/tex]

Determining the y-intercept (b)

The slope-intercept form of the line equation is given by

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

where

From the graph, we can figure out the y-intercept by checking the value of y at x = 0.

If we closely check the graph, at x = 0, the value of y = 3

Therefore, the y-intercept b = 3

Slope-intercept Equation

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

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

substituting b = 3 and m = -1/2

[tex]y\:=\:-\frac{1}{2}x+3[/tex]

Therefore, the slope-intercept equation of the line is:  [tex]y\:=\:-\frac{1}{2}x+3[/tex]

The graph is also attached below.

help I can’t do basic math skjsjdmdmx

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Piper has a flower shop. She started the week with 320 flowers. Each day she sells half of the flowers in her shop.
Which graph shows the exponential decay described?
320
280
240
Flowers 200
Left
160
120
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40
320
280
240
Flowers 200
Left
160
120
80
40
OA
Oc.
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Days
0 1 2 3 4 5 6
Days
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280
240
Flowers 200
Left
160
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