Download presentation

Presentation is loading. Please wait.

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

Similar presentations

© 2024 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google