how would I write an equation for the following linear relationships:
(x5,y20),(x10,y30)(x15,y40)(x20,y50)(x25,y50)(x30,y50)
That is one linear relationship from x=5 to x=20. For x > 20; y = 50. That is a second linear relationship.
It is a piecewise continuous function
y = 2x + 10 (5 < x <or = 20)
y = 50 (20 < x < 30)
10. Which of the following is the equation of a line that passes through (-2, -1) and (-4, -3)?
To write an equation for a linear relationship, you need to identify the pattern and then use that pattern to create a suitable equation.
Looking at the given coordinates, you can observe that the x-values (or inputs) increase by 5 units every time, and the y-values (or outputs) increase by 10 units after every increment of 5 in the x-values. Additionally, when x = 25, y remains constant at 50. This tells us that there is a horizontal line after x = 25.
Let’s break down the given examples:
1. (x5, y20): This is our starting point, where x = 5 and y = 20.
- This point gives us the y-intercept of the equation.
2. (x10, y30): As x increases by 5 (from x = 5 to x = 10), y increases by 10 (from y = 20 to y = 30).
- This gives us the slope of the equation, which is the "rise over run" between any two points on a line.
3. (x15, y40): Similar to the previous step, the slope is still 10 (as y increments by 10) when x increases by 5 (from x = 10 to x = 15).
4. (x20, y50): Again, the slope remains 10 when x increases by 5 (from x = 15 to x = 20), and y increases by 10 (from y = 40 to y = 50).
5. (x25, y50): Here, we notice that the y-value remains constant at 50 while the x-value continues to increase. This implies a horizontal line after x = 25.
6. (x30, y50): Similar to the previous point, the y-value remains constant at 50 while x increases.
To summarize, we deduce that the equation for this linear relationship consists of a slope of 10 and a y-intercept of 20 since the line starts at (x5, y20). Considering the horizontal line after x = 25, we can write the equation as follows:
y = 10x + 20 for x ≤ 25
y = 50 for x > 25
This equation will give us the corresponding y-values for any given x-value in this linear relationship.