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

in the graph, range of the x axis is minus five to five by increment of one and minus four, minus two, two, and four are labeled. the range of y axis is minus thee to five by increment of one and minus two, two and four are labeled. in the graph, line passes through the points (1, 1) and (0, 4).

a. 3x − y = 4
b. 3x + y = 4
c. −3x − y = 4
d. −3x + y = 4

B. 3x +y = 4

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.

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