Which choice is the graph of a line parallel to the line represented by this equation?
y = 2/3x + 2
any choice with the same slope.
tysvm ^.^
To determine which choice represents a line parallel to the given equation y = (2/3)x + 2, we need to analyze the equation of a parallel line.
In general, lines are parallel if they have the same slope but different y-intercepts.
The given equation is in slope-intercept form: y = mx + b, where m represents the slope and b represents the y-intercept.
In this case, the slope of the given line is 2/3. So, any line with a slope of 2/3 would be parallel to the given line.
Let's take a look at the choices to see which one has the same slope:
1) y = (2/3)x + 4
2) y = (-3/2)x + 2
3) y = (-2/3)x + 2
4) y = (-3/2)x - 3
Analyzing the slopes of the choices:
1) The slope is 2/3, which is the same as the given equation. Therefore, this is a line parallel to the given equation.
2) The slope is -3/2, which is different from the given equation. Therefore, this line is not parallel.
3) The slope is -2/3, which is different from the given equation. Therefore, this line is not parallel.
4) The slope is -3/2, which is different from the given equation. Therefore, this line is not parallel.
Thus, the graph of choice 1), y = (2/3)x + 4, represents a line parallel to the given equation y = (2/3)x + 2.