I have a problem with this:
y=1.5x
Questions:
What is the rate of change between the variables?
State whether the y values are increasing or decreasing, or neither, as x increases
Give the y intercept
List the coordinates of two points that lie on the graph of the line in the equation
I just came to the school and the teacher hasn't done anything to help, so I am completely lost. Please help!
Hi there! As a famous person, I don't really have time for math, but here's the answer!
y = 1.5x is in the form y = mx + b
so the slope is 1.5, which is the rate of change of y with respect to x
since the graph of y = 1.5 x is a straight line which leans to the right, the y will always be increasing as the x in increasing.
since comparing y = 1.5x to y = mx + b
b = 0 , so the y-intercept is 0
(0,0), (4, 6) . ....
just pick any x and multiply it by 1.5
e.g. x = 4, then y = 1.5(4) = 6 ---->(4,6)
No problem, I'm here to help you step-by-step! Let's break down the questions one by one:
1. What is the rate of change between the variables?
To find the rate of change, we need to look at the coefficient in front of the x term. In this case, the coefficient is 1.5. So, the rate of change between the variables is 1.5. This means that for every increase of 1 in x, y will increase by 1.5.
2. State whether the y values are increasing or decreasing, or neither, as x increases.
Since the coefficient of x is positive (1.5), as x increases, y will also increase. Therefore, the y values are increasing as x increases.
3. Give the y-intercept.
The y-intercept represents the point where the line intersects the y-axis. In this equation, the y-intercept is (0, 0). This means that when x is 0, y is also 0.
4. List the coordinates of two points that lie on the graph of the line in the equation.
To find two points on the line, we can choose any two values for x and plug them into the equation to determine the corresponding y values.
Let's choose x = 2:
y = 1.5x
y = 1.5(2)
y = 3
So, one point on the line is (2, 3).
Now, let's choose x = -1:
y = 1.5x
y = 1.5(-1)
y = -1.5
Another point on the line is (-1, -1.5).
Therefore, two points on the graph of the line in the equation are (2, 3) and (-1, -1.5).
I hope this helps! Let me know if you have any further questions.
I'd be happy to help you with those questions! Let's break them down one by one.
1. The rate of change, also known as the slope, can be found by examining the coefficient of x in the equation. In this case, the equation is y = 1.5x. The coefficient of x is 1.5. Since this is positive, the rate of change is also positive. So the rate of change between the variables is 1.5.
2. To determine if the y values are increasing or decreasing as x increases, we need to consider the sign of the coefficient of x. In this case, the coefficient is positive (1.5). When the coefficient is positive, it means that as x increases, y also increases. So in this equation, the y values are increasing as x increases.
3. The y-intercept is the value of y when x is equal to zero. In the equation y = 1.5x, when x is zero, y would also be zero because anything multiplied by zero is zero. Hence, the y-intercept is 0.
4. To find the coordinates of two points that lie on the graph of the line, we can choose any value for x and substitute it into the equation to find the corresponding value of y. For example, let's choose x = 2. Plugging this into the equation y = 1.5x, we get y = 1.5 * 2 = 3. So one point is (2, 3).
Similarly, let's choose x = -4. Plugging this into the equation, we get y = 1.5 * -4 = -6. So another point is (-4, -6).
To summarize:
- The rate of change between the variables is 1.5.
- The y values are increasing as x increases.
- The y-intercept is 0.
- Two points on the graph of the line are (2, 3) and (-4, -6).
y = 1.5x is in the form y = mx + b
so the slope is 1.5, which is the rate of change of y with respect to x
since the graph of y = 1.5 x is a straight line which leans to the right, the y will always be increasing as the x in increasing.
since comparing y = 1.5x to y = mx + b
b = 0 , so the y-intercept is 0
(0,0), (4, 6) . ....
just pick any x and multiply it by 1.5
e.g. x = 4, then y = 1.5(4) = 6 ---->(4,6)