Question

Please help (picture is linked)

Answer 1

Answer:

$\LARGE\mathsf{slope\:=\:\frac{9}{5}}$

y-intercept: (0, 32), b = 32

$\LARGE\mathsf{y\:=\:\frac{9}{5}x\:+\:32}$

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.

Slope

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:

$\LARGE\mathsf{m = \frac {(y_2\: -\: y_1)}{(x_2\: -\: x_1)}}$

$\LARGE\mathsf{m = \frac {(212\: -\: 32)}{(100\: -\: 0)}\:= \frac {180}{100}}$

$\LARGE\mathsf{m\:=\:\frac{9}{5}}$

Therefore, the slope of the line is  $\LARGE\mathsf{m\:=\:\frac{9}{5}}$.

Y-intercept:

Next, the given problem asks for the value of the y-intercept.  The y-intercept is the point on the graph where it crosses the y-axis, with its coordinates occurring at point, (0, b ). 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, $\LARGE\mathsf{m\:=\:\frac{9}{5}}$, and substitute these values into the slope-intercept form, y = mx + b:

y = mx + b

$\LARGE\mathsf{212\:=\:\frac{9}{5}(100)\:+\+b}$

212 = 180 + b

Subtract 180 from both sides to isolate b:

212 - 180 = 180 - 180 + b

32 = b

The y-intercept is (0, 32), where b = 32.

Slope-intercept form:

Given the slope, $\LARGE\mathsf{m\:=\:\frac{9}{5}}$,  and the y-intercept, b = 32:

The linear equation in slope-intercept form is:  $\LARGE\mathsf{y\:=\:\frac{9}{5}x\:+\:32}$