Respuesta :

Catya
y-intercept, where the graph crosses y-axiss is 0. that means in the equation: y = mx + b
b = 0
the m, is slope. looking at the graph you can see the points on the line are connect up 4 right 1. rise/run = slope = 4
y = 4x

Answer:  The correct option is (D) [tex]y=4x.[/tex]

Step-by-step explanation:  We are given to select the equation represented by the graph shown.

From the graph, we see a straight line passing through the points (0, 0) and (1, 4).

The slope of a straight line passing through the points (a, b) and (c, d) is given by

[tex]m=\dfrac{d-b}{c-a}.[/tex]

So, the slope of the graphed line will be

[tex]m=\dfrac{4-0}{1-0}\\\\\Rightarrow m=\dfrac{4}{1}\\\\\Rightarrow m=4.[/tex]

Since the line passes through the point (0, 0), so its equation will be

[tex]y-0=m(x-0)\\\\\Rightarrow y=4\times x\\\\\Rightarrow y=4x.[/tex]

Thus, the required equation that represents the graphed line is [tex]y=4x.[/tex]

Option (D) is CORRECT.

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