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Line m in the xy-plane contains the poin...

Line m in the xy-plane contains the points (2, 4) and (0, 1).Which of the following is an equation of line m ?

A

y = 2x + 3

B

y = 2x + 4

C

`y=3/2x+3`

D

`y=3/2x+1`

Text Solution

Verified by Experts

The correct Answer is:
D
The slope-intercept form of a linear equation is y = ax + b, where a is the slope of the graph of the equation and b is the y-coordinate of the y-intercept of the graph. Two ordered pairs `(x_1, y_1)` and `(x_2, y_2)` can be used to compute the slope of the line with the formula `a = (y_2-y_1)/(x_2-x_1)` . Substituting the two ordered pairs (2,4) and (0,1) into this formula gives `a=(4-1)/(2-0)`, which simplifies to `3/2`. Substituting this value for a in the slope-intercept form of the equation yields `y=3/2x+b`. Substituting values from the ordered pair (0,1) into this equation yields `1=3/2(0)+b`, so b =1. Substituting the value for b in the slope -intercept equation yields `y=3/2x+1`.
Choice A is incorrect. This may result from misinterpreting the change in x-values as the slope and misinterpreting the change in y-values as the y-coordinate of the y-intercept of the graph. Choice B is incorrect and may result from using the x- and y-values of one of the given points as the slope and y-coordinate of the y-intercept, respectively. Choice C is incorrect. This equation has the correct slope but the incorrect y-coordinate of the y-intercept.
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