On this part, we’re going to see easy methods to write linear equations from the given conditions and graphs in slope-intercept kind.

The slope-intercept type of the equation is y = mx + b, the place “m” is slope and “b” is y-intercept. And y-intercept is nothing however the level at which the road cuts y-axis.

For instance, if the road cuts y-axis at (0, -4), then the y-intercept is -4.

Instance 1 :

The lease charged for area in an workplace constructing is a linear relationship associated to the scale of the area rented. At west important avenue workplace leases, $750 lease charged for 600 sq. ft of area and $1150 lease charged for 900 sq. ft of area. Write an equation in slope-intercept kind for the lease at West Most important Avenue Workplace Leases.

Answer :

Step 1 :

Establish the impartial and dependent variables.

The impartial variable (x) is the sq. footage of flooring area.

The dependent variable (y) is the month-to-month lease.

Step 2 :

Write the data given in the issue as ordered pairs.

The lease for 600 sq. ft of flooring area is $750 :

(600, 750)

The lease for 900 sq. ft of flooring area is $1150 :

(900, 1150)

Step 3 :

Discover the slope.

m = (y_{2} – y_{1})/(x_{2} – x_{1})

Substitute :

(x_{1}, y_{1}) = (600, 750)

(x_{2}, y_{2}) = (900, 1150)

Then,

m = (1150 – 750)/(900 – 600)

m = 400/300

m = 4/3

Step 4 :

Discover the y-intercept.

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

Slope-intercept kind :

y = mx + b

Substitute 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 kind

y = mx + b

Substitute m = 4/3 and b = -50.

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

y = (4/3)x – 50

Instance 2 :

Hari’s weekly allowance varies relying on the variety of chores he does. He acquired $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 kind.

Answer :

Step 1 :

Establish the impartial and dependent variables.

The impartial variable (x) is variety of chores Hari does per week.

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

Step 2 :

Write the data given in the issue as ordered pairs.

For 12 chores, he receives $16 allowance :

(12, 16)

For 8 chores, he receives $14 allowance :

(8, 14)

Step 3 :

Discover the slope.

m = (y_{2} – y_{1})/(x_{2} – x_{1})

Substitute :

(x_{1}, y_{1}) = (12, 16)

(x_{2}, y_{2}) = (8, 14)

Then,

m = (14 – 16)/(8 – 12)

m = (-2)/(-4)

m = 1/2

m = 0.5

Step 4 :

Discover the y-intercept.

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

Slope-intercept kind :

y = mx + b

Substitute 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 kind

y = mx + b

Substitute m = 0.5 and b = 10.

y = 0.5x + 10

Instance 3 :

A video membership costs a one-time membership charge plus a rental charge for every DVD borrowed. Use the graph to write down an equation in slope-intercept kind to characterize the quantity spent, y, on x DVD leases.

Answer :

Step 1 :

Select two factors on the graph, (x_{1}, y_{1}) and (x_{2}, y_{2}), to search out the slope.

Discover the ratio between change in y-values and change in x.

m = (y_{2} – y_{1}) / (x_{2} – x_{1})

Substitute :

(x_{1}, y_{1}) = (0, 8)

(x_{2}, y_{2}) = (8, 18)

Then,

m = (18 – 8)/(8 – 0)

m = 10/8

m = 1.25

Step 2 :

Learn the y-intercept from the graph. That’s, the purpose at which the road cuts y-axis.

The y-intercept is 8.

b = 8

Step 3 :

Allow us to use slope (m) and y-intercept (b) values to write down an equation in slope-intercept kind.

y = mx + b (Slope-intercept kind)

Substitute m = 1.25 and b = 8.

y = 1.25x + 8

Instance 4 :

The money register subtracts $2.50 from a $25 Espresso Café present card for each medium espresso the client buys. Use the graph to write down an equation in slope-intercept kind to characterize this case.

Answer :

Step 1 :

Select two factors on the graph, (x₁, y₁) and (x₂, y₂), to search out the slope.

Discover the ratio between change in y-values and change in x.

m = (y_{2} – y_{1})/(x_{2} – x_{1})

Substitute :

(x_{1}, y_{1}) = (0, 25)

(x_{2}, y_{2}) = (10, 0)

Then,

m = (0 – 25)/(10 – 0)

m = -25/10

m = -2.5

Step 2 :

Learn the y-intercept from the graph. That’s, the purpose at which the road cuts y-axis.

The y-intercept is 25.

Step 3 :

Allow us to use slope (m) and y-intercept (b) values to write down an equation in slope-intercept kind.

y = -2.5x + 25 (Slope-intercept kind)

Substitute m = -2.5 and b = 25.

y = -2.5x + 25

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