Fill in the missing number to complete the linear equation that gives the rule for this table. Explain/show how you got your ans
wer in
as much detail as you can.
as much detail as you can.
1 answer:
Answer:
y = x - 1
Step-by-step explanation:
To create a linear equation in the slope-intercept form, which is in the form of y = mx + b, we need to find the slope/rate of change, m, and the y-intercept, b.
Rate of change can be calculated using two pairs, (3, 2) and (4, 3)
Rate of change/slope (m) = ,
Where,
b = 4
f(b) = 3
a = 3
f(a) = 2
Plug in the values
m = 1
Plug in x = 3, y = 2 and m = 1 into y = mx + b
2 = 1(3) + b
Solve for b
2 = 3 + b
Subtract 3 from each side
2 - 3 = b
-1 = b
b = -1
Substitute m = 1 and b = -1 into y = mx + b.
y = 1(x) +(-1)
y = x - 1
The linear equation that gives the rule for this table is y = x - 1
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Answer:
2.4 hours or 2 hours and 24 minutes
Step-by-step explanation:
Jack mows 1/6 of the lawn per hour while Marilyn mows 1/4 of the lawn together. Adding up those rates yields in their combined mowing rate:
The time required for them to mow the entire lawn is:
It would take them both 2.4 hours to mow the lawn together.
The statement " <span>y </span>varies directly as <span>x </span>," means that when <span>x </span>increases,<span>y </span>increases by the same factor. In other words, <span>y </span>and <span>x </span>always have the same ratio:
<span>where </span><span>k </span>is the constant of variation.
<span>We can also express the relationship between </span><span>x </span><span>and </span><span>y </span>as:
<span><span>y = kx</span> </span>
<span>where </span><span>k </span>is the constant of variation.
Since <span>k </span>is constant (the same for every point), we can find <span>k </span>when given any point by dividing the y-coordinate by the x-coordinate. For example, if <span>y </span>varies directly as <span>x </span>, and <span>y = 6</span> when <span>x = 2</span> , the constant of variation is <span>k = = 3</span> . Thus, the equation describing this direct variation is <span>y = 3x </span>.
Example 1: If <span>y </span>varies directly as <span>x </span>, and <span>x = 12</span> when <span>y = 9</span> , what is the equation that describes this direct variation?
<span>k = = </span>
<span>y = x</span>
Example 2: If <span>y </span>varies directly as <span>x </span>, and the constant of variation is <span>k = </span>, what is <span>y </span>when <span>x = 9</span> ?
<span>y = x = (9) = 15</span>
As previously stated, <span>k </span>is constant for every point; i.e., the ratio between the <span>y </span>-coordinate of a point and the <span>x </span>-coordinate of a point is constant. Thus, given any two points <span>(x 1, y 1)</span> and <span>(x 2, y 2)</span> that satisfy the equation, <span> = k </span>and <span> = k </span>. Consequently, <span> = </span>for any two points that satisfy the equation.
Example 3: If <span>y </span>varies directly as <span>x </span>, and <span>y = 15</span> when <span>x = 10</span> , then what is <span>y </span>when <span>x = 6</span> ?
<span> = </span>
<span> = </span>
<span>6() = y </span>
<span>y = 9</span>
