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You observe that the line shown below passes through the point (0,4 )and has a slope of 1/2. You choose (x,y) as an arbitrary point on the line other than (0,4) and use the fact that the slope of a line is constant to write which equation?

You observe that the line shown below passes through the point 04 and has a slope of 12 You choose xy as an arbitrary point on the line other than 04 and use th class=
You observe that the line shown below passes through the point 04 and has a slope of 12 You choose xy as an arbitrary point on the line other than 04 and use th class=

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kudzordzifrancis

Answer:

[tex]y= \frac{1}{2}x + 4[/tex]

Step-by-step explanation:

The given line passes through the point (0,4) and has a slope of ½.

If we choose an arbitrary point (x,y) on the line, the slope of this line is given by:

[tex] \frac{y - 4}{x - 0} [/tex]

Since the slope of a straight line is constant, the above expression for the slope must be equal to ½.

This implies that:

[tex] \frac{y - 4}{x - 0} = \frac{1}{2} [/tex]

We simplify to get:

[tex] \frac{y - 4}{x} = \frac{1}{2} [/tex]

This implies that:

[tex]y - 4 = \frac{1}{2} x[/tex]

The equation of this line is therefore:

[tex]y = \frac{1}{2}x + 4[/tex]