Make an equation

Question

Make an equation that passes through points (0,32) and (100, 212). Then use this equation to find the Celsius temperature at 70°F.

Answer 1

Q: Make an equation that passes through points (0,32) and (100, 212). Then use this equation to find the Celsius temperature at 70°F.

To start this problem, we want to find the slope. This tells us how steep our graph is, and represents m in the equation y = mx + b. Slope is calculated by rise over run. This means how much the graph moves up in the y direction for every 1 unit that the graph moves over in the x direction.

We calculate slope or rise over run with the equation rise/run.If we have two point, (x_a , y_a) and ( x_b , y_b )

slope = m= (y_b - y_a)/(x_b - x_a). If we have two points, (0, 32) and (100, 212) then m = (212-32)/ (100-0) = 190/100 = 1.9. Since the y axis is Degrees Fahrenheit and the x axis is Degrees Celsius, our slope 1.9 means an increase of 1.9 degrees Fahrenheit for every increase of 1 degree Celsius.

m = 1.9 Degrees F/degree C

Let's go back to our equation, y = mx + b. Now, we can plug in 1.9 Degrees F/degree C for m.

y = 1.9x + b. Now, let's use two (x, y) coordinates to solve for the y-intercept, b. The y-intercept tells us what the y-value is when x = 0.

We have the point (0, 32) where x is 0 and y is 32, so this problem already gave us our y-intercept. So, our b = 32. We can even check this using the point (100, 212).

212 = 1.9(100) + 32 = 190 + 32 = 212.

Now we know y = 1.9x + 32. Let's use this to find the x Celsius temperature when y Fahrenheit temperature equals 70 degrees.

70 = 1.9x +32 To solve, we need to always perform the same operation to each side.

We want to end up with x = some number, so it's a good idea to get all numbers away form x. We start with any subtraction or addition. To get rid of 32 and move it to the left side of the equals sign, we need to do the opposite operation (subtraction).

70 = 1.9x + 32

-32 -32

38 0

38 = 1.9x Now we have 38 = 1.9x. Since x is multiplied by 1.9, we need to divide each side by 1.9.

/1.9 /1.9

20 = x Once we do this, we get our answer x = 20. We must pay attention to the units- x = 20 degrees Celsius.

When the temperature is 70 degrees fahrenheit, the temperature in celsius is 20 degrees

Answer 2

This will be a linear equation, and you are given two points on the graph. You can use those two points to find the slope, and then use one of the points in the point - slope formula to get the equation.

First, the slope is the change of y divided by the change of x. Mathematically that is (y₂ - y₁)/(x₂ - x₁). The points are (0,32) and (100,212), so plugging those into the formula gives:

(212-32)/(100-0) = 180/100 = 1.8,

Now choose the coordinates of either point and plug them into (y-y₁) = m(x-x₁). Let's use (0,32). The math is always easy with zero.

y - 32 = m(x - 0), substitute 1.8 from above for the slope:

y - 32 = 1.8x. Then add 32 to each side to solve for y

y = 1.8x + 32.

The point (0,32) describes the relationship between Fahrenheit and Celsius at the freezing point.In other words ) degrees Celsius is equal to 32 degrees Fahrenheit. So in the equation we just derived, the x value is Celsius and the y value is Fahrenheit.

We need to find the Celsius value of 70 degrees Fahrenheit using the equation. Fahrenheit is y, so we get:

70 = 1.8x + 32, subtract 32 from each side

38 = 1.8x, now divide both sides by 1.8 to get the Celsius value (x):

38/1.8 = 21.11 degrees Celsius

Hope that helps

Answer 3

The relationship between Fahrenheit and Celsius temperatures is linear.

Slope = (212-32) / (100-0) = 9/5

F = (9/5)(C) + b

32 = (9/5)(0) + b So, b = 32

F = (9/5)C + 32

When C = 70, F = (9/5)(70) + 32 = 158