Answer:
(c) y = -3x +6
Explanation:
The equation can be written in slope-intercept form when we know the slope and the y-intercept.
Slope-intercept form
The slope-intercept form of the equation of a line is ...
y = mx +b . . . . . . where m is the slope and b is the y-intercept
Y-intercept
The y-intercept is the y-value where the line crosses the y-axis. It is 6. This eliminates choices A and D, leaving choices ...
- y = 3x +6 . . . . . choice B
- y = -3x +6 . . . . .choice C
Slope
The line goes down to the right. This is a negative slope, eliminating choice B.
The equation of the line is y = -3x +6.
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Additional comment
The line intersects the x-axis at x=2. This means the "rise" of the line is -6 units for a "run" of 2 units. The numerical value of the slope is ...
m = rise/run = -6/2 = -3
Now, we know the parameters of the equation are m=-3, b=6, and the equation of the line is
y =-3x +6