Question 1

Solve the problem.
-In 1995 the United States recovered 27% of its municipal wastes through recycling, up from 17% in 1990. Find a linear equation that fits this data. Use this equation to predict the percentage recycled in 2004.

Accepted Answer

The answer of Solve the problem.
-In 1995 the United States...

Question 2

Write the equation of the line, with the given properties, in slope-intercept form.
-Slope =  through (4, 8)

Accepted Answer

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. We are given the slope as 11ebb63d_1bad_3bbf_b851_7dd0152c8f23_TB8475_11 and a point on the line as (4,8). 
Using the point-slope formula, we get:
y - y1 = m(x - x1)
y - 8 = 11ebb63d_1bad_3bbf_b851_7dd0152c8f23_TB8475_11(x - 4)
y - 8 = 11ebb63d_1bad_3bbf_b851_7dd0152c8f23_TB8475_11x - 11ebb63d_1bad_62d2_b851_7b1dc55ea018_TB8475_11
y = 11ebb63d_1bad_62d1_b851_1f846a68bb12_TB8475_11x + 11ebb63d_1bad_62d2_b851_7b1dc55ea018_TB8475_11
Thus, the equation of the line in slope-intercept form is y = 11ebb63d_1bad_62d1_b851_1f846a68bb12_TB8475_11x + 11ebb63d_1bad_62d2_b851_7b1dc55ea018_TB8475_11. The slope-intercept form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept. We are given that the slope is 11ebb63d_1bad_3bbf_b851_7dd0152c8f23_TB8475_11 and the point (4,8) lies on the line. We can use the point-slope formula to find the equation of the line:
(y - 8) = 11ebb63d_1bad_3bbf_b851_7dd0152c8f23_TB8475_11(x - 4)
Simplifying, we get:
y = 11ebb63d_1bad_3bbf_b851_7dd0152c8f23_TB8475_11x - 11ebb63d_1bad_62d1_b851_1f846a68bb12_TB8475_11
So the y-intercept is -11ebb63d_1bad_62d1_b851_1f846a68bb12_TB8475_11. Therefore, the equation of the line in slope-intercept form is y = 11ebb63d_1bad_3bbf_b851_7dd0152c8f23_TB8475_11x - 11ebb63d_1bad_62d1_b851_1f846a68bb12_TB8475_11, which corresponds to choice B.

Question 3

Write the equation of the line, with the given properties, in slope-intercept form.
-Through (-6, -6) and (-8, -5)

Accepted Answer

First, we need to find the slope of the line using the two given points.

m = (y2 - y1) / (x2 - x1) = (-5 - (-6)) / (-8 - (-6)) = 1/2

Now we can use the point-slope formula to find the equation of the line:

y - y1 = m(x - x1)

Using point (-6, -6):

y + 6 = (1/2)(x + 6)

Simplifying:

y = (1/2)x - 9

This is in slope-intercept form (y = mx + b), so the answer is A.

Question 4

Write the equation of the line, with the given properties, in slope-intercept form.
-Through (7, 3) and (-5, -4)

Accepted Answer

The answer of Write the equation of the line, with...

Question 5

Write the equation of the line, with the given properties, in slope-intercept form.
-Slope = -2, through (7, 3)

Accepted Answer

The slope-intercept form of a line is y = mx + b, where m is the slope. Given the slope is -2 and the line passes through (7, 3), substitute these into the equation to find b: 3 = -2(7) + b, which gives b = 17. Thus, the equation is y = -2x + 17.

Quiz 4: Graphing Linear Equations

Solve the problem. -In 1995 the United States recovered 27% of its municipal wastes through recycling, up from 17% in 1990. Find a linear equation that fits this data. Use this equation to predict the percentage recycled in 2004.

Write the equation of the line, with the given properties, in slope-intercept form. -Slope = through (4, 8)

Write the equation of the line, with the given properties, in slope-intercept form. -Through (-6, -6) and (-8, -5)

Write the equation of the line, with the given properties, in slope-intercept form. -Through (7, 3) and (-5, -4)

Write the equation of the line, with the given properties, in slope-intercept form. -Slope = -2, through (7, 3)