Answer :
Sure, let's break down the problem step-by-step to find the vertical intercept.
We are provided with two points from the table:
- When the total square feet [tex]\( h = 0 \)[/tex], the total cost [tex]\( c = \$2000 \)[/tex].
- When the total square feet [tex]\( h = 5000 \)[/tex], the total cost [tex]\( c = \$527,000 \)[/tex].
Since the relationship between the square footage and the total cost is linear, we can write the equation of the line in the slope-intercept form:
[tex]\[ c = mh + b \][/tex]
where [tex]\( m \)[/tex] is the slope, and [tex]\( b \)[/tex] is the vertical intercept.
### Step 1: Finding the Slope ([tex]\(m\)[/tex])
The slope of a line ([tex]\(m\)[/tex]) between two points [tex]\((h_1, c_1)\)[/tex] and [tex]\((h_2, c_2)\)[/tex] is calculated as:
[tex]\[ m = \frac{c_2 - c_1}{h_2 - h_1} \][/tex]
Substituting the given points:
[tex]\[ m = \frac{527000 - 2000}{5000 - 0} \][/tex]
[tex]\[ m = \frac{525000}{5000} \][/tex]
[tex]\[ m = 105 \][/tex]
### Step 2: Finding the Vertical Intercept ([tex]\(b\)[/tex])
The vertical intercept ([tex]\(b\)[/tex]) is the value of [tex]\(c\)[/tex] when [tex]\(h = 0\)[/tex]. From the table, when [tex]\(h = 0\)[/tex], [tex]\(c = 2000\)[/tex].
So, our vertical intercept ([tex]\(b\)[/tex]) is:
[tex]\[ b = 2000 \][/tex]
### Conclusion: Vertical Intercept
The vertical intercept in the ordered pair form is:
[tex]\[ (0, 2000) \][/tex]
Thus, the vertical intercept of the line containing the given points is [tex]\( (0, 2000) \)[/tex].
We are provided with two points from the table:
- When the total square feet [tex]\( h = 0 \)[/tex], the total cost [tex]\( c = \$2000 \)[/tex].
- When the total square feet [tex]\( h = 5000 \)[/tex], the total cost [tex]\( c = \$527,000 \)[/tex].
Since the relationship between the square footage and the total cost is linear, we can write the equation of the line in the slope-intercept form:
[tex]\[ c = mh + b \][/tex]
where [tex]\( m \)[/tex] is the slope, and [tex]\( b \)[/tex] is the vertical intercept.
### Step 1: Finding the Slope ([tex]\(m\)[/tex])
The slope of a line ([tex]\(m\)[/tex]) between two points [tex]\((h_1, c_1)\)[/tex] and [tex]\((h_2, c_2)\)[/tex] is calculated as:
[tex]\[ m = \frac{c_2 - c_1}{h_2 - h_1} \][/tex]
Substituting the given points:
[tex]\[ m = \frac{527000 - 2000}{5000 - 0} \][/tex]
[tex]\[ m = \frac{525000}{5000} \][/tex]
[tex]\[ m = 105 \][/tex]
### Step 2: Finding the Vertical Intercept ([tex]\(b\)[/tex])
The vertical intercept ([tex]\(b\)[/tex]) is the value of [tex]\(c\)[/tex] when [tex]\(h = 0\)[/tex]. From the table, when [tex]\(h = 0\)[/tex], [tex]\(c = 2000\)[/tex].
So, our vertical intercept ([tex]\(b\)[/tex]) is:
[tex]\[ b = 2000 \][/tex]
### Conclusion: Vertical Intercept
The vertical intercept in the ordered pair form is:
[tex]\[ (0, 2000) \][/tex]
Thus, the vertical intercept of the line containing the given points is [tex]\( (0, 2000) \)[/tex].
