Exercise 124 Page 49

Equations in slope-intercept form follow a certain format.

y=mx+ b In this format m is the slope and b is the y-intercept. The line has a slope of -5, which means that we can substitute m=-5. y=-5x+ b To write a complete equation for this line, we also need to determine the y-intercept, b. We can do that by substituting the given point (2,8) into the equation and solving for b.

y=-5x+b

SubstituteII

x= 2, y= 8

8=-5( 2)+b

▼

Solve for b

MultNegPos

(- a)b = - ab

8=-10+b

AddEqn

LHS+10=RHS+10

18=b

RearrangeEqn

Rearrange equation

b= 18

Now that we have both the slope and the y-intercept, we can write the final equation. y=-5x+ 18 ⇔ y=-5x+ 18

An equation in slope-intercept form follows a specific format.

y= mx+b For an equation in this form, m is the slope and b is the y-intercept. Let's use the given points to calculate m. We will start by substituting the points into the Slope Formula.

m=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( -3,4) & ( 5,-4)

m=-4- 4/5-( -3)

▼

Simplify right-hand side

SubNeg

a-(- b)=a+b

m=-4-4/5+3

AddSubTerms

Add and subtract terms

m=-8/8

MoveNegNumToFrac

Put minus sign in front of fraction

m=-8/8

CalcQuot

Calculate quotient

m=-1

A slope of -1 means that for every 1 horizontal step in the positive direction, we take 1 vertical step in the negative direction. Now that we know the slope, we can write a partial version of the equation. y= -1 x+b ⇒ y=- x+b To complete the equation, we also need to determine the y-intercept, b. Since we know that the given points will satisfy the equation, we can substitute one of them into the equation to solve for b. Let's use ( -3, 4).

y=- x+b

SubstituteII

x= -3, y= 4

4=-( -3)+b

▼

Solve for b

NegNeg

- (- a)=a

4=3+b

SubEqn

LHS-3=RHS-3

1=b

RearrangeEqn

Rearrange equation

b=1

A y-intercept of 1 means that the line crosses the y-axis at the point (0,1). We can now complete the equation. y= -1x+1 ⇒ y=- x+1

An equation in slope-intercept form follows a specific format.

y= mx+b For an equation in this form, m is the slope and b is the y-intercept. Let's use the given points to calculate m. We will start by substituting the points into the Slope Formula.

m=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( -2,4) & ( 4,-5)

m=-5- 4/4-( -2)

▼

Simplify right-hand side

SubNeg

a-(- b)=a+b

m=-5-4/4+2

AddSubTerms

Add and subtract terms

m=-9/6

MoveNegNumToFrac

Put minus sign in front of fraction

m=-9/6

ReduceFrac

a/b=.a /3./.b /3.

m=-3/2

A slope of - 32 means that for every 2 horizontal steps in the positive direction, we take 3 vertical steps in the negative direction. Now that we know the slope, we can write a partial version of the equation. y= -3/2 x+b To complete the equation, we also need to determine the y-intercept, b. Since we know that the given points will satisfy the equation, we can substitute one of them into the equation to solve for b. Let's use ( -2, 4).

y=-3/2x+b

SubstituteII

x= -2, y= 4

4=-3/2( -2)+b

▼

Solve for b

MultNegNegOnePar

- a(- b)=a* b

4=3/2(2)+b

FracMultDenomToNumber

a/2* 2 = a

4=3+b