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Equations and Graphing

Please show work so that I may understand. Thank you.

1.) Solve the equation x + 0.04x = 9600

2.) Solve the inequality (1/6) x - 1 ≤ 4 + (1/3) x.

Express answer in both graphical
and interval notation form.

Find the missing coordinates

y = -x + 4

x y
-2
0
2
0
-2

3.) Plot at least five points for this equation

x + 4y = 5

4.) Graph the line

(-2,5) with slope - 1

5.) Write each equation in standard form using only integers.

½ x - 9 = 0

6.) Determine whether the lines are parallel, perpendicular or neither.

y = 1/3x + ½
y = 1/3x - 2

7.) The percentage of women in the 20-24 age group who have never married went from 55% in 1970 to 73% in 2000. Let 1970 be year 0 and 2000 be year 30.

1.) Find and intercept the slope of the line through the points (0,55) and (30, 73)
2.) Find the equation of the line in part 1
3.) What is the meaning of the y-intercept
4.) Use the equation to predict the percentage in 2010
5.) If this trend continues, then in what year will the percentage of women in the
20-24 age group who have never married reach 100%.
8.) Write this equation in slope-intercept form

2x + 3y = 90

9.) Find the equation of each line in the form y = mx + b if possible.

The line through the origin that is perpendicular to the line through (-3,0) and (0,-3).

10.) The median age at first marriage for females increased from 24.5 years in 1995 to
25.1 years in 2000. Let 1995 be year 5 and 2000 be year 10

1.) Find the equation of the line through (5,24,5) and (10,25,1)
2.) What do x and y represent in your equation
3.) Intercept the slope of this line
4.) In what year will the median age be 30.
5.) Graph the equation.

11.) Graph each inequality

2x - y + 3 > 0

4x + 3y > 24 ( use the test point method)

12.) Excess pectin makes juice cloudy. In one test, the chemist measures the concentration of the enzyme, c, in milligrams per milliliter and the fraction of light absorbed by the liquid, a. If a > 0.07c + 0.02, then the enzyme is working as it should. Graph the inequality in the first quadrant.

Solution Preview

1.) Solve the equation x + 0.04x = 9600
Add like terms: x + 0,04x = 1.04x, so 1.04x = 9600.
Divide both sides by the coefficient of the variable: 1.04x / 1.04 = x, 9600 / 1.04 = 9230.8 so x = 9230.8

2.) Solve the inequality (1/6) x - 1 ≤ 4 + (1/3) x.

Express answer in both graphical
and interval notation form.

Subtract 1/6 x from both sides: -1 ≤ 4 + 1/6 x
Subtract 4 from both sides: -4 ≤ 1/6 x
Divide both sides by 1/6: -24 ≤ x

Interval notation: x ≥ -24
Graphical: A number line with a closed dot on -24 and shaded to the left.

Find the missing coordinates

y = -x + 4

x y
-2 6 - (-2) + 4 = 2 + 4
0 4 -0 + 4
2 2 -2 + 4
0 4 -0 + 4
-2 6 - (-2) + 4 = 2 + 4

For this, plug the given x coordinates into the equation as done above.

3.) Plot at least five points for this equation

x + 4y = 5

Choose values that fit. One way to do this is to solve the equation for x: x = 5 - 4y and then choose values for y to calculate the corresponding x.
Y = 0, x = 5 - 4*0 = 5-0 = 5
Y=1, x = 5-4 = 1
Y = 2, x = 5-8 = -3
Y = 3, x = 5-12 = -7
Y = 4, x = 5 - 16 = -11

4.) Graph the line

(-2,5) with slope - 1

Slope is rise over run, so a slope of - 1 means the line goes down 1 for every step to the right. This would be a line through (-2, 5) that goes diagonally through ...

Solution Summary

This provides examples of a variety of problems regarding equations and graphing, including parallel/perpendicular lines, finding slope, creating equations, interpreting intercepts, and using equations to predict values.

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