1. Daily Homework Quiz
Review 5.3
Write an equation in point-slope form of the line that passes through (6, –4) and has slope 2. 1.
y – y1 = m(x – x1)
ANSWER
y + 4 = 2(x – 6)
Write an equation in point-slope form of the line that passes through (–1, –6) and (3, 10). 2.
ANSWER
y + 6 = 4(x + 1) or y –10 = 4(x–3)

2. Review 5.3
Write an equation in point-slope form of the line that passes through the given points.
1. (1, 4), (6, –1)
NOW PUT EACH ANSWER IN SLOPE-INTERCEPT FORM!!
ANSWER
y – 4 = –1(x – 1) or y + 1 = –1(x – 6)
y – 4 = – x or y + 1 = - x + 6
y = – x or y = - x + 5
2. (
–1, –2), (2, 7)
ANSWER
y + 2 = 3(x + 1) or y – 7 = 3(x – 2)
y + 2 = 3x or y – 7 = 3x – 6
y = 3x or y = 3x + 1

3. 5.4 Write Linear Equations in Standard Form

4. Convert this equation into standard form:
Ax + By = C
1.)
Multiply everything by 5
Move over the “x” term
-2x x
I CAN’T LEAD WITH A NEGATIVE!!!
So let’s change the sign of each term.
It’s kind of like moving backwards!

5. Convert this equation into standard form:
Ax + By = C
2.)
+ x x
Move over the “x” term

6. Convert this equation into standard form:
Ax + By = C
3.)
Multiply everything by 2
Move over the “x” term
+ 1x x

7. Convert this equation into standard form:
Ax + By = C
4.)
Multiply everything by 3
Move over the “x” term
-2x x
I CAN’T LEAD WITH A NEGATIVE!!!
So let’s change the sign of each term.

8. Write an equation of the line in STANDARD FORM using the information given.
5.) m = 2 and (3,-2)
Start with Point-Slope Form
Now put into slope-intercept form
Now put into Standard form
-2x x
No LEADING NEGATIVES!
Change all the signs of each term

9. Write an equation of the line in STANDARD FORM using the information given.
5.) m = and (4,-5)
Start with Point-Slope Form
Now put into slope-intercept form
Now put into Standard form
Multiply everything by 2
- 3x x
No LEADING NEGATIVES!
Change all the signs of each term

10. Every one get communicators with a blank side!!!

11. Write an equation of the line in STANDARD FORM using the information given.
Start with Point-Slope Form
Now put into slope-intercept form
Now put into Standard form
Multiply everything by 4
+1x x
No LEADING NEGATIVES!
Change all the signs of each term

12. Write the point-slope form of the line that passes through (4,3) and (1,2)

13. Write the slope-intercept form of the line that passes through (4,5) and (1,-1)

14. Write an equation of the line in STANDARD FORM using the information given.
5.) m = and (-4,3)
Start with Point-Slope Form
Now put into slope-intercept form
Now put into Standard form
+ 2x x

15. Write an equation of the line in STANDARD FORM using the information given.
5.) m = and (3,-5)
Start with Point-Slope Form
Now put into slope-intercept form
Now put into Standard form
Multiply everything by 2
- 3x x
No LEADING NEGATIVES!
Change all the signs of each term

16. Write an equation of the line in STANDARD FORM using the information given.
Start with Point-Slope Form
Now put into slope-intercept form
Now put into Standard form
Multiply everything by 4
+ 3x x

17. Write an equation of the line in STANDARD FORM using the information given.
Start with Point-Slope Form
Now put into slope-intercept form
Now put into Standard form
Multiply everything by 2
+ 5x x

18. Write an equation from a graph
EXAMPLE 2
Write an equation from a graph
Write an equation in standard form of the line shown.
SOLUTION
STEP 1
Calculate the slope. –3
m =
1 – (–2)
1 – 2 = 3 –1
STEP 2
Write an equation in point-slope form. Use (1, 1).
y – y1 = m(x – x1)
Write point-slope form.
y – 1 = –3(x – 1)
Substitute 1 for y1, 3 for m and 1 for x1.

19. Write an equation from a graph
EXAMPLE 2
Write an equation from a graph
STEP 3
Rewrite the equation in standard form.
3x + y = 4
Simplify. Collect variable terms on one side, constants on the other.

20. EXAMPLE 2
Write an equation from a graph
GUIDED PRACTICE
for Examples 1 and 2
Write an equation in standard form of the line through (3, –1) and (2, –3). 2.
–2x + y = –7
ANSWER

21. Complete an equation in standard form
EXAMPLE 3
EXAMPLE 4
EXAMPLE 4
Complete an equation in standard form
Find the missing coefficient in the equation of the line shown. Write the completed equation.
SOLUTION
STEP 1
Find the value of A. Substitute the coordinates of the given point for x and y in the equation. Solve for A.
Ax + 3y = 2
Write equation.
A(–1) + 3(0) = 2
Substitute –1 for x and 0 for y.
–A = 2
Simplify.
A = –2
Divide by –1.

22. Complete an equation in standard form
EXAMPLE 4
Complete an equation in standard form
STEP 2
Complete the equation.
–2x + 3y = 2
Substitute –2 for A.

23. GUIDED PRACTICE
for Examples 3 and 4
Write equations of the horizontal and vertical lines that pass through the given point.
3. (–8, –9)
y = –9, x = –8
ANSWER

24. GUIDED PRACTICE
for Examples 3 and 4
Write equations of the horizontal and vertical lines that pass through the given point.
4. (13, –5)
y = –5, x = 13
ANSWER

25. EXAMPLE 4
EXAMPLE 3
Complete an equation in standard form
GUIDED PRACTICE
Write an equation of a line
for Examples 3 and 4
Find the missing coefficient in the equation of the line that passes through the given point. Write the completed equation.
–4x + By = 7, (–1, 1)
ANSWER
3; –4x + 3y = 7

26. EXAMPLE 1
Write equivalent equations in standard form
Write two equations in standard form that are equivalent to 2x – 6y = 4.
SOLUTION
To write one equivalent equation, multiply each side by 2.
To write another equivalent equation, multiply each side by 0.5.
4x – 12y = 8
x – 3y = 2

27. EXAMPLE 1
GUIDED PRACTICE
for Examples 1 and 2
Write two equations in standard form that are equivalent to x – y = 3. 1.
2x – 2y = 6,
3x – 3y = 9
ANSWER

28. EXAMPLE 5
Solve a multi-step problem
ANSWER
The equation 8s + 12l = 144 models the possible combinations.
b. Find the intercepts of the graph.
Substitute 0 for s.
8(0) + 12l = 144
l = 12
Substitute 0 for l.
8s + 12(0) = 144
s = 18

29. EXAMPLE 4
EXAMPLE 3
Complete an equation in standard form
GUIDED PRACTICE
Write an equation of a line
for Examples 3 and 4
Find the missing coefficient in the equation of the line that passes through the given point. Write the completed equation.
Ax + y = –3, (2, 11)
ANSWER
–7; –7x +y = –3