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The equation of a line that passes through (0, 4) and (2, 3) is y = 1/2x + 4.

A) True
B) False

1 Answer

4 votes

Final answer:

The correct equation of the line passing through (0, 4) and (2, 3) is y = (-1/2)x + 4, as calculated using the slope formula. The provided equation y = 1/2x + 4 is incorrect; hence, the statement is False.

Step-by-step explanation:

The equation of a line that passes through (0, 4) and (2, 3) is y = 1/2x + 4. To verify this, we can find the slope (m) of the line using the two given points. The slope is calculated by taking the difference in the y coordinates, divided by the difference in the x coordinates:

m = (y2 - y1) / (x2 - x1) = (3 - 4) / (2 - 0) = -1 / 2

Next, we use one of the points and the slope to write the equation of the line in the slope-intercept form, which is y = mx + b. Using the point (0, 4), where b is the y-intercept (the y-coordinate when x=0), we get:

y = (-1/2)x + 4

The correct equation of the line is therefore y = (-1/2)x + 4, and not y = 1/2x + 4. The given statement is False.

User Florin Marcus
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