Exercise 69 Page 328

In order to write both the slope-intercept form and the point-slope form, we need the slope of the line. To find the slope, we will use the given points and the Slope Formula. Now that we know the slope, let's form our equations. We will find them one at a time.

Point-Slope Form

Equations in point-slope form follow a specific format. y- y_1= m(x- x_1) In this form, m is the slope of the line and ( x_1, y_1) is a point on the line. Since we know the slope of the line is - 58, we can write the equation of the line in point-slope form. We can use either of the given points as (x_1,y_1) in our equation. Let's use ( 5, -1).

y-y_1=m(x-x_1)

SubstituteValues

Substitute values

y-( -1)= -5/8(x- 5)

SubNeg

a-(- b)=a+b

y+1=- 5/8(x-5)

Please note that any point on the line can be used to form a point-slope equation. Therefore, our equation is only one of infinitely many possible equations!

Slope-Intercept Form

Equations in slope-intercept form also follow a specific format. y= mx+b, In this form, m represents the slope of the line and b represents the y-intercept. We already calculated the slope as m= - 58 above. The next step is to substitute one of the points into the equation and solve for the y-intercept, b. Let's use the point ( 5, -1).

y=-5/8x+b

SubstituteII

x= 5, y= -1

-1=-5/8* 5+b

▼

Solve for b

MoveRightFacToNum

a/c* b = a* b/c

-1=-25/8+b

AddEqn

LHS+25/8=RHS+25/8

-1+25/8=b

OneToFrac

Rewrite 1 as 8/8

-8/8+25/8=b

AddFrac

Add fractions

17/8=b

RearrangeEqn

Rearrange equation

b=17/8

Now that we know the y-intercept lies at (0,178), we have what we need to write a slope-intercept form equation. y= -5/8x+17/8