Answer:
y-intercept: (0, 32), b = 32
Step-by-step explanation:
Given (0, 32) as the freezing point of water in Celsius and Farenheit, and (100, 212) as the boiling point of water in Celsius and Farenheit.
<h2><u>Slope</u></h2>
Use these points to solve for the slope of their line.
Let (x₁, y₁) = (0, 32)
(x₂, y₂) = (100, 212)
Substitute these points into the following formula for the slope:
Therefore, the <u>slope</u> of the line is .
<h2><u>Y-intercept:</u></h2>
Next, the given problem asks for the value of the y-intercept. The <u>y-intercept</u> is the point on the graph where it crosses the y-axis, with its coordinates occurring at point, (0, <em>b </em>). Thus, the y-intercept provides the value of y when its corresponding x-coordinate is 0.
To solve for the y-intercept, b, we must choose one of the given points, (100, 212), and the slope, , and substitute these values into the <u>slope-intercept form</u>, y = mx + b:
y = mx + b
212 = 180 + b
Subtract 180 from both sides to isolate <em>b</em>:
212 - 180 = 180 - 180 + b
32 = b
The <u>y-intercept</u> is (0, 32), where <em>b</em> = 32.
<h2><u>Slope-intercept form:</u></h2>
Given the <u>slope</u>, , and the <u>y-intercept</u>, <em>b</em> = 32:
The linear equation in slope-intercept form is: