Question

Pls help with 1-6 pls !!

1. Write an equation in slope-intercept form of the line given the slope=" 1/4 pass through
(-2,1).

2. Write an equation in slope-intercept form of the line that passes through (0,4) and (5,19)

3. Write a linear function f with the given values.
a. g(0) = 2, f (2) = -3
b. g (-4) = -5, g (3) = - 1.

4. The corresponding data for electricity generated by hydropower are 248 million megawatt hours in 2007 and 277 million megawatt hours in 2012. Write a linear model that represents the number of megawatt hours generated by hydropower as a function of the number of years since 2007.

5. Write an equation in point-slope form of the line that passes through (-2, -5) and (4, -1).
6. In a city, if a customer is charged $12 for using 1,000 gallons and $16 for using 1,800
gallons.

a. Write a linear model that represents the monthly cost for water as a function of the number of gallons you will used.

b. Find the cost of 2,000 gallons.

Answer 1

See below, and note the interpretation of the question.

Explanation:

See the attached image for a graph of all the lines and points.

1. Write an equation in slope-intercept form of the line given the slope=" 1/4 pass through (-2,1).

1. Look for an equation of the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x is zero).

We are given the slope, so use that for m: y = (1/4)x + b.

We need a value of b that forces the line through point (-2,1). This can be done by entering the point into the above equation and solving for b:

y = (1/4)x + b

1 = (1/4)*(-2) + b [for (-2,1)]

1 = -0.5+ b

b = 1.5

The equation is y = (1/4)x + 1.5

2. Write an equation in slope-intercept form of the line that passes through (0,4) and (5,19)

1. Look for an equation of the form y=mx+b

2. Determine the slope by calculating the Rise and Run of the two given points:

Going from (0,4) to (5,19):

Rise = 19-4 = 15

Run = 5 - 0 = 5

Rise/Run, or slope, m = (15/5) or 3

The equation with the slope of 5:

y = 5x+b

3. To find b, enter either of the 2 points into the equation and solve for b:

y = 5x+b

4 = 5*(0)+b for (0,4)

b = 4

The equation is y=5x+4

3. Write a linear function f with the given values.

Are the expressions written correctly? I see f and g. I'll assume the forst two are meant to be f, and the last two a new function, g(x).:

a. f(0) = 2, f(2) = -3

b. g(-4) = -5, g(3) = - 1.

These results supply us with 2 points for each function [line]:

f: (0,2) and (2,-3)

g: (-4,-5) and (3,-1)

We can use these two points to find the slope for lines f and g:

f: (0,2) and (2,-3)

Rise = -3 - 2 = -5

Run = 2 - 0 = 2

Slope = (-5/2) or -2.5

The equation for f is y = (-2.5)x + b

Enter one of the 2 points to find b:

y = (-2.5)x + b

y = (-2.5)*(0) + b for (0,2)

2 = b

The equation for f is f(x) = -2.5x+2

Do the same for g:

(-4,-5) and (3,-1)

Rise = (-1 - (-5)) = 4

Run = (3 - (-4)) = 7

Slope = 4/7 or 0.571

y = 0.571x + b

Substituting point (3,-1) and solving for b:

-1 = 0.571*(3) + b

b = -2.71

The equation for g is g(x) = 0.571c-2.71

See the attached image.