Question

The donations by a restaurant to a certain charity, y, will be two-fifths of its profits, x, plus $50. How can you determine the equation in slope-intercept form that shows the relationship between x and y without graphing the line?

Answer 1

Slope intercept form:

`y=(2)/(5)x+50`

Step-by-step explanation:

The donations by a restaurant to a certain charity, y

Profit of the restaurant, $x

The donation is two-fifth of the profit and $50

According to the question,

`y=(2)/(5)x+50`

Slope intercept form:

y = mx + b

where, m is slope and b is y-intercept.

Now, we will compare the equation.

`y=(2)/(5)x+50\Rightarrow y=mx+b`

`m\rightarrow (2)/(5)`

`b\rightarrow 50`

Hence, The slope intercept form of the given statement is
`y=(2)/(5)x+50`

Answer 2

The equation would be y=(2/5)x+50.

Step-by-step explanation:
Slope-intercept form is given by y=mx+b, where m is the slope and b is the y-intercept. The original $50 donated has nothing to do with the profits; if the profits are $0, they will still donate $50. This is the y-intercept, b.

Since they are donating 2/5 of their profits x, this means that the rate of change, or slope, of the line will be 2/5 of a dollar donated per dollar profit; this is m. Plugging these in gives us the equation above.