is y= -4x+3 proportional or non proportional
The Correct Answer and Explanation is:
The equation y=−4x+3y = -4x + 3y=−4x+3 is non-proportional.
To understand why, we need to define what proportional and non-proportional relationships are. A proportional relationship is one where two variables, say yyy and xxx, are related in such a way that the ratio yx\frac{y}{x}xy remains constant for all values of xxx and yyy. This is often represented by the equation y=kxy = kxy=kx, where kkk is a constant of proportionality. The graph of a proportional relationship is a straight line that passes through the origin (0, 0), because when x=0x = 0x=0, y=0y = 0y=0.
In contrast, a non-proportional relationship has a graph that is a straight line but does not pass through the origin. It has a non-zero y-intercept, which means that when x=0x = 0x=0, the value of yyy is not zero. This is exactly the case for the equation y=−4x+3y = -4x + 3y=−4x+3, where the y-intercept is 333.
Let’s break this down:
- The equation is in slope-intercept form, y=mx+by = mx + by=mx+b, where mmm represents the slope, and bbb represents the y-intercept.
- In y=−4x+3y = -4x + 3y=−4x+3, the slope is −4-4−4, and the y-intercept is 333.
- When x=0x = 0x=0, y=3y = 3y=3. This means the graph crosses the y-axis at y=3y = 3y=3, which clearly shows that the relationship does not go through the origin.
Since the ratio of yyy to xxx is not constant and the graph does not pass through the origin, this equation represents a non-proportional relationship.
