Given the function of the graph.
The slope is 1.5
What is the positive domain?
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Given the function of the graph.
The slope is 1.5
What is the positive domain?
To find the domain of positivity, we need to find the point of intersection of the equation with the x-axis.
For this, we need to find the formula of the equation.
We know that a linear equation is constructed as follows:
Y=MX+B
m represents the slope of the line, which is given to us: 1.5
b represents the point of intersection of the line with the Y-axis, which can be extracted from the existing point on the graph, -8.
And therefore:
Y=1.5X-8
Now, we replace:
Y=0, since we are trying to find the point of intersection with the X-axis.
0=1.5X-8
8=1.5X
5.3333 = X
We reveal that the point of intersection with the X-axis is five and one third (5.333)
Now, as we know that the slope is positive and the function is increasing, we can conclude that the domain of positivity is when the x values are less than five and one third.
That is:
5.333>X
And this is the solution!
Look at the linear function represented in the diagram.
When is the function positive?
The positive domain refers to the x-values where the function output (y-values) is positive. You need to find where the line is above the x-axis.
Setting y = 0 finds the x-intercept - the boundary point where the function changes from positive to negative (or vice versa). This is your reference point!
Look at the slope! If slope is positive (like 1.5), the line goes up from left to right. So the function is positive on the left side of the x-intercept.
Both expressions mean the same thing! reads as "5⅓ is greater than x" which is equivalent to "x is less than 5⅓".
That's correct too! These are all the same value written in different forms.
Test a point! Pick an x-value less than 5⅓ (like x = 0) and substitute: y = 1.5(0) - 8 = -8. Wait, that's negative! Check your work - the function is actually negative when x < 5⅓.
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