Use the graph to interpret and match the approximate intervals with their descriptions.
1 answer:
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Answer: Any real number x as long as and
In other words, anything but 0 or -2/3 is valid.
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Explanation:
Set the denominator equal to zero and solve for x
2(3x^2 + 2x) = 0
3x^2 + 2x = 0
x(3x + 2) = 0
x = 0 or 3x+2 = 0 .... zero product property
x = 0 or 3x = -2
x = 0 or x = -2/3
If either x = 0 or x = -2/3, then the denominator 2(3x^2 + 2x) will be zero. But recall that we cannot have zero in the denominator. Dividing by zero is not allowed. The expression is undefined when we divide by zero.
Therefore, we must exclude x = 0 and x = -2/3 from the domain. Any other real number is valid as an x input.
Answer:
slope-intercept:
point-slope:
Step-by-step explanation:
The slope-intercept form of a line is written as y = mx + b, where m is the slope and b is the y-intercept.
The point-slope form of a line is written as y - y1 = m(x - x1), where (x1, y1) is a given point and m is the slope.
Here, we see that the slope is -4/5, which means that m = -4/5. Since we're given a point (-3, 2), let's go ahead and just write the point-slope form already. (x1, y1) = (-3, 2) so x1 = -3 and y1 = 2. Then:
y - y1 = m(x - x1)
y - 2 = (-4/5) * (x + 3)
Now, we want to find the slope-intercept form, so we need to figure out the y-intercept. Well, first, let's plug in what we know:
y = mx + b
y = (-4/5)x + b
Any point on this line will satisfy the above equation. Since (-3, 2) is on this line, if we plug -3 in for x and 2 in for y, the equation should hold true, so we can solve for b:
y = (-4/5)x + b
2 = (-4/5) * (-3) + b
2 = 12/5 + b
b = -2/5
So, the y-intercept is -2/5. Then the slope-intercept form is:
Thus, our two equations are:
slope-intercept:
point-slope: