Write an equation in slope intercept form for $750 and $600 and $1150

y = 0.5x + 10

Step-by-step explanation:

Step 1:

Identify the independent and dependent variables.

The independent variable (x) is the square footage of floor space.

The dependent variable (y) is the monthly rent.

Step 2:

Write the information given in the problem as ordered pairs.

The rent for 600 square feet of floor space is $750:

(600, 750)

The rent for 900 square feet of floor space is $1150:

(900, 1150)

Step 3:

Find the slope.

m = (y₂ - y₁) / (x₂ - x₁)

Substitute (600, 750) for (x₁, y₁) and (900, 1150) for (x₂, y₂).

m = (1150 - 750) / (900 - 600)

m = 400 / 300

m = 4/3

Step 4:

Find the y-intercept.

Use the slope 4/3 and one of the ordered pairs (600, 750).

Slope-intercept form:

y = mx + b

Plug m = 4/3, x = 600 and y = 750.

750 = (4/3) (600) + b

750 = (4) (200) + b

750 = 800 + b

-50 = b

Step 5:

Substitute the slope and y-intercept.

Slope-intercept form

y = mx + b

Plug m = 4/3 and b = - 50

y = (4/3) x + (-50)

y = (4/3) x - 50

Problem 2:

Hari's weekly allowance varies depending on the number of chores he does. He received $16 in allowance the week he did 12 chores, and $14 in allowance the week he did 8 chores. Write an equation for his allowance in slope-intercept form.

Solution:

Step 1:

Identify the independent and dependent variables.

The independent variable (x) is number of chores Hari does per week

The dependent variable (y) is the allowance he receives per week.

Step 2:

Write the information given in the problem as ordered pairs.

For 12 chores, he receives $16 allowance:

(12, 16)

For 8 chores, he receives $14 allowance:

(8, 14)

Step 3:

Find the slope.

m = (y₂ - y₁) / (x₂ - x₁)

Substitute (12, 16) for (x₁, y₁) and (8, 14) for (x₂, y₂).

m = (14 - 16) / (8 - 12)

m = (-2) / (-4)

m = 1/2

m = 0.5

Step 4:

Find the y-intercept.

Use the slope 0.5 and one of the ordered pairs (8, 14).

Slope-intercept form:

y = mx + b

Plug m = 0.5, x = 8 and y = 14.

14 = (0.5) (8) + b

14 = 4 + b

10 = b

Step 5:

Substitute the slope and y-intercept.

Slope-intercept form

y = mx + b

Plug m = 0.5 and b = 10

y = 0.5x + 10