Write the slope-intercept form of the equation of each line given the slope and y-intercept.
a. slope= 5, y-intercept= -3

b. slope= -1, y-intercept= 5

2. write the point-slope form of the equation of the line through the given point with the given slope.
a. point= (5,3), slope= 4/5

b. point= (-3,-2), slope= -2/3

3. write the slope-intercept form of the equation of the line described.
a. point= (1,-1), parallel to y=-6x+1

b. point= (4,5), parallel to y=1/2x+3

4. write the standard from of the equation of the line through the given point with the given slope.
a. point=(-4,4), slope= -7/4

b. point=(1,2), slope= 6

4b. −6x + y = −4

4a. 7x + 4y = −12

3b. y = ½x + 3

3a. y = −6x + 5

2b. y + 2 = −⅔(x + 3)

2a. y - 3 = ⅘(x - 5)

1b. y = -x + 5

1a. y = 5x - 3

Step-by-step explanation:

4.

Plug the coordinates into the Slope-Intercept Formula first, then convert to Standard Form [Ax + By = C]:

b.

2 = 6[1] + b

6

−4 = b

y = 6x - 4

-6x - 6x

−6x + y = −4 >> Standard Equation

a.

4 = −7⁄4[-4] + b

7

−3 = b

y = −7⁄4x - 3

+7⁄4x +7⁄4x

7⁄4x + y = −3 [We do not want fractions in our Standard Equation, so multiply by the denominator to get rid of it.]

4[7⁄4x + y = −3]

7x + 4y = −12 >> Standard Equation

3.

Plug both coordinates into the Slope-Intercept Formula:

b.

5 = ½[4] + b

2

3 = b

y = ½x + 3 >> EXACT SAME EQUATION

a.

−1 = −6[1] + b

−6

5 = b

y = −6x + 5

* Parallel lines have SIMILAR RATE OF CHANGES [SLOPES].

2.

b. y + 2 = −⅔(x + 3)

a. y - 3 = ⅘(x - 5)

According to the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE TERMS OF WHAT THEY REALLY ARE, so be EXTREMELY CAREFUL inserting the coordinates into the formula with their CORRECT SIGNS.

1.

b. y = -x + 5

a. y = 5x - 3

Just write out the Slope-Intercept Formula as it is given to you.

I am joyous to assist you anytime.