# Graphing, Writing Equations and Inequalities (Math Problem Sample)

Complete the following problems using the Case 3 Answer Template.

Here are some formulas and equations you will use in this section. Slope: m = change in y = y2-y1 change in x x2–x1 Slope-intercept form: y = mx + b Point-slope form: y-y1= m(x-x1) Standard form: Ax + By = C; where A is a positive value Find the slope of the points. Reduce to lowest terms. 1. (0, -2) (4, 6) 2. (7, 3) (9, 3) 3. (5, 2) (1, 5) 4. (12, 4) (12, 6) Identify the slope and y-intercept in the following equations. 5. 2x+3y=8 6. 6x=y+1 Write an equation of a vertical line passing through the point (6, 3).

Write an equation of a horizontal line passing through the point (2, 8). Write an equation of a line in slope-intercept form with a slope of -4 and passing through the point (0, -3).

Write an equation of a line in slope-intercept form with a slope of 1/2 and passing through the point (0, 6). Write an equation of a line in point-slope form with a slope of -3/4 and passing through the point (1, -5). Write an equation of a line in standard form with a slope of -8 and passing through the point (-10, 2). Write an equation of a line passing through the points (-2, -1) and (0, 4). Write the final answer in slope-intercept form. Write an equation of a line passing through the points (-3, 6) and (-5, 3). Write the final answer in slope-intercept form. Graph the following equations and inequalities on a coordinate plane, shading the solution set where necessary. Note: When completing this assignment in the Case 3 Answer Template, go to "insert" and "shapes." Choose the circles for the points and the lines to connect the dots. Use the arrows to represent the shading. For example: 15. y= 4x-2 16. 2x+5y=10 17. x=3 and y=6 18. 3x+5y ≤ 15 19. y < -2x-3 20. x > 4 and y ≤ -1

source..Graphing, Writing Equations and Inequalities

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MAT101 Case 3 Answer Template

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Instructor:

Use this template to insert your answers for the assignment. Please use one of the four methods for showing your work (EE, Math Type, ALT keys, or neatly typed). Remember that your work should be clear and legible.

Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible.

Slope: m= change in y = y2-y1

change in x x2-x1

Slope-intercept form:y=mx+b

Point-slope form:y-y1=m(x-x1)

Standard form:Ax+By=C; where A is a positive value

Find the slope of the points. Reduce to lowest terms.

1. (0, -2) (4, 6)

Calculations:

Slope= Change in y/ change in x

= (6—2)/ (4-0)=8/4

Answer: ___2____________

2. (7, 3) (9, 3)

Calculations:

Slope= Change in y/ change in x

=(3-3)/ 9-7)=0/ 2

Answer: _0______________

3. (5, 2) (1, 5)

Calculations:

Slope= Change in y/ change in x

= (5-2)/(1-5)= 3/-4

Answer: _______-3/4________

4. (12, 4) (12, 6)

Calculations:

Slope= Change in y/ change in x

=(6-4)/ (12-12)=2/0

Answer: _____undefined__________

Identify the slope and y-intercept in the following equations.

5. 2x+3y=8

Calculations:

Y=mx+c

3y=-2x+8

Y= (-2x+8)/3

Answer: slope=__-2/3_______y-intercept=_8/3________

6. 6x=y+1

Calculations:

Y=mx+c

Y+1=6x

Y=6x-1

Answer: slope=__6_______y-intercept=__-1_______

7. Write an equation of a vertical line passing through the point (6, 3).

For a vertical line the change in x is zero.

Slope is undefined being Change in y/ 0

X=b and 6=b

Answer: __x=6_____________

8. Write an equation of a horizontal line passing through the point (2, 8).

Y=b and b=8

Answer: ___y=8___________

9. Write an equation of a line in slope-intercept form with a slope of -4 and passing through the point (0, -3).

Calculations:

Change in Y= y- -3 and change in X= x-0

Y+3/x=-4

Answer: ___y= -4x-3____________

10. Write an equation of a line in slope-intercept form with a slope of QUOTE and passing through the point (0, 6).

Calculations:

Change in Y=6-y and change in x= 0-x

6-y/-x=1/2

2(6-y)=-x

12-2y= -x

Answer: ____y=1/2x+6___________

11. Write an equation of a line in point-slope form with a slope of QUOTE and passing through the point (1, -5).

Calculations:

y- -5/ x-1= -3/4

y+5/ x-1=-3/4

4(y+5)=-3 (x-1)

y+5= (-3x +3)/4

y=-3x/4+ ¾-20/4

y=-3x/4 -17/4

y-y1=m (x-x1)

Answer: ___y- (-5) =-3/4(x-1) ____________

12. Write an equation of a line in standard form with a slope of QUOTE and passing through the point (-10, 2).

Calculations:

y-2/ (x- -10)=-8

y=-8(x+10)

y= -8x-80+2 hence y=-8x-78

Answer: __8x+y= -78____________

13. Write an equation of a line passing through the points (-2, -1) and (0, 4). Write the final answer in slope-intercept form.

Calculations:

Slope= (4—1)/ (0—2)=5/2=2.5

Y=2.5x+c

To get c, then 4= 2.5(0) +c hence

C=4

Answer: __y=2.5x+4_____________

14. Write an equation of a line passing through the points (-3, 6) and (-5, 3). Write the final answer in slope-intercept form.

Calculations:

M=(6-3)/- (-3- -5)= 3/2

C=6-(3/2*-3)=21/2=10.5

Answer: y=1.5x+10.5_______________

Graph the following equations and inequalities on a coordinate plane, shading the solution set where necessary.

Go to ‘insert’ and ‘shapes’. Choose the circles for the points and the lines to connect the dots. Use the arrows to represent the shading.

For example:

15. y= 4x-2

Calculations:...

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