Linear Equations in Standard Form Examples
Learn how to convert equations from different forms to standard form, solve for x and y intercepts, and write equations in standard form using given information. The examples provided cover various scenarios and guide you step-by-step through the process, with clear explanations and visuals to help you understand and practice standard form equations.
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Presentation Transcript
5.4 Standard form Obj: I can write an equation of a line in standard form. Write down new HW. Ch 5 Retests are available in WIN.(offer expires Friday and Im out tomorrow) Warm up: Convert from point slope form to slope intercept form y-5 = -3(x-10) Find the x and y intercepts to -4x + 8y =16
5.4 Write Linear Equations in Standard Form
Convert this equation into standard form: 1.) y =2 5x 3 Ax + By = C Multiply everything by 5 5y =2x 15 Move over the x term -2x -2x I CAN T LEAD WITH A NEGATIVE!!! So let s change the sign of each term. 2x+5y = 15 It s kind of like moving backwards! 2x 5y =15
Convert this equation into standard form: 2.) y = x+5 Ax + By = C + x + x Move over the x term x+y =5
Convert this equation into standard form: 3.) 2x +7 Ax + By = C y = 1 Multiply everything by 2 2y = 1x+14 Move over the x term + 1x + 1x x+2y =14
Convert this equation into standard form: 4.) 3x +4 Ax + By = C y =2 Multiply everything by 3 3y =2x+12 Move over the x term -2x -2x I CAN T LEAD WITH A NEGATIVE!!! So let s change the sign of each term. 2x+3y =12 2x 3y = 12
Write an equation of the line in STANDARD FORM using the information given. 5.) m = 2 and (3,-2) y y1= m(x x1) y+2 =2(x 3) y+2=2x 6 Start with Point-Slope Form Now put into slope-intercept form -2 -2 y =2x 8 Now put into Standard form -2x -2x = + y 2 12 x No LEADING NEGATIVES! Change all the signs of each term y = 2 8 x
Write an equation of the line in STANDARD FORM using the information given. 3 2 5.) m = and (4,-5) y y1= m(x x1) y +5 =3 2(x 4) y +5 =3 - 5 - 5 y =3 2x 11 Start with Point-Slope Form Now put into slope-intercept form 2x 6 Now put into Standard form 2y =3x 22 Multiply everything by 2 - 3x - 3x 3x+2y = 22 No LEADING NEGATIVES! Change all the signs of each term 3x 2y =22
Write an equation of the line in STANDARD FORM using the information given. m =3 4 0 4= 1 5.) (-4,4) and (0,3) 4 y y1= m(x x1) y 4 = 1 4(x +4) y 4 = 1 + 4 + 4 y = 1 4x +3 Start with Point-Slope Form Now put into slope-intercept form 4x 1 Now put into Standard form 4y = 1x+12 Multiply everything by 4 +1x +1x x+4y =12 No LEADING NEGATIVES! Change all the signs of each term
Write the point-slope form of the line that passes through (4,3) and (1,2)
Write the slope-intercept form of the line that passes through (4,5) and (1,-1)
Write an equation of the line in STANDARD FORM using the information given. 5.) m = -2 and (-4,3) y y1= m(x x1) y 3= 2(x+4) Start with Point-Slope Form Now put into slope-intercept form y 3= 2x 8 + 3 + 3 y = 2x 5 + 2x + 2x Now put into Standard form 2x+y = 5
Write an equation of the line in STANDARD FORM using the information given. 5.) m = -3 and (3,-5) y y1= m(x x1) y +5 =3 2(x 4) y +5 =3 - 5 - 5 y =3 2x 11 Start with Point-Slope Form Now put into slope-intercept form 2x 6 Now put into Standard form 2y =3x 22 Multiply everything by 2 - 3x - 3x 3x+2y = 22 No LEADING NEGATIVES! Change all the signs of each term 3x 2y =22
Write an equation of the line in STANDARD FORM using the information given. m =3 0 0 4= 4= 3 3 5.) (4,0) and (0,3) 4 y y1= m(x x1) y 0 = 3 4(x 4) y = 3 4x +3 Start with Point-Slope Form Now put into slope-intercept form Now put into Standard form 4y = 3x+12 Multiply everything by 4 + 3x + 3x 3x+4y =12
Write an equation of the line in STANDARD FORM using the information given. m =5 0 2= 5 0 2=5 5.) (2,0) and (0,5) 2 y y1= m(x x1) y 0 = 5 2(x 2) y = 5 Start with Point-Slope Form Now put into slope-intercept form 2x +5 Now put into Standard form 2y = 5x+10 Multiply everything by 2 + 5x + 5x 5x+2y =10
EXAMPLE 2 2 Write an equation from a graph Write an equation in standard form of the line shown. SOLUTION STEP1 Calculate the slope. m=1 ( 2) 3 3 = = 1 1 2 STEP2 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.
EXAMPLE 2 2 Write an equation from a graph STEP3 Rewrite the equation in standard form. 3x + y = 4 Simplify. Collect variable terms on one side, constants on the other.
EXAMPLE 2 2 GUIDED PRACTICE Write an equation from a graph for Examples 1 and 2 2. Write an equation in standard form of the line through (3, 1) and (2, 3). ANSWER 2x + y = 7
EXAMPLE 4 EXAMPLE 3 EXAMPLE 4 Complete an equation in standard form Find the missing coefficient in the equation of the line shown. Write the completed equation. SOLUTION STEP1 Find the value of A. Substitute the coordinates of the given point for xandyin the equation. Solve forA. Ax + 3y = 2 A( 1) + 3(0) = 2 Write equation. Substitute 1 for x and 0 for y. Simplify. Divide by 1. A = 2 A = 2
EXAMPLE 4 Complete an equation in standard form STEP2 Complete the equation. 2x + 3y = 2 Substitute 2 for A.
for Examples 3 and 4 GUIDED PRACTICE Write equations of the horizontal and vertical lines that pass through the given point. 3. ( 8, 9) y= 9, x= 8 ANSWER
for Examples 3 and 4 GUIDED PRACTICE Write equations of the horizontal and vertical lines that pass through the given point. 4. (13, 5) y= 5, x= 13 ANSWER
EXAMPLE 4 EXAMPLE 3 GUIDED PRACTICE Complete an equation in standard form 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. 5. 4x + By = 7, ( 1, 1) ANSWER 3; 4x + 3y = 7
EXAMPLE 1 Write equivalent equations in standard form Write two equations in standard form that are equivalent to 2x 6y =4. SOLUTION To write another equivalent equation, multiply each side by 0.5. To write one equivalent equation, multiply each side by 2. 4x 12y =8 x 3y = 2
EXAMPLE 1 GUIDED PRACTICE for Examples 1 and 2 1. Write two equations in standard form that are equivalent to x y =3. 2x 2y =6, 3x 3y = 9 ANSWER
Solve a multi-step problem EXAMPLE 5 ANSWER The equation 8s+12l=144 models the possible combinations. b. Find the intercepts of the graph. Substitute0fors. 8(0) + 12l = 144 l = 12 Substitute 0 for l. 8s + 12(0) = 144 s = 18
EXAMPLE 4 EXAMPLE 3 GUIDED PRACTICE Complete an equation in standard form 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. 6.Ax + y = 3, (2, 11) ANSWER 7; 7x +y = 3
