Question

Which of the following is an equation of the line in the graph?

Answer 1

Answer:

B. 3x +y = 4

Step-by-step explanation:

It is perhaps easiest to simply try the equations to see which one works.

For x=0, there are two different kinds of answers:

... A and C: -y = 4

... B and D: y = 4

Since we know y=4 when x=0 (from the point (0, 4)), we can eliminate choices A and C.

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Using the point (1, 1), you can try choices B and D to see which works:

... B: 3·1 +1 = 4 . . . . true (put 1 where x and y are in the equation)

... D: -3·1 +1 = -2 = 4 . . . . false

The appropriate choice is the equation of B: 3x +y = 4.

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Derive the equation from the given points

There are several ways you can derive the equation. Since you have the y-intercept (the point with x=0), you can use the slope-intercept form to start.

The slope (m) is ...

... m = (change in y)/(change in x) = (4 -1)/(0 -1)

... m = -3

We know the y-intercept (b) is 4, so the slope-intercept form of the equation is ...

... y = mx +b

... y = -3x +4

Adding 3x puts this in standard form:

... 3x +y = 4