The equation of the line that goes through the point ( 4 , 5 ) and is parallel to the line 3 x + 4 y = 3 can be written in the form y = m x + b

Question

The equation of the line that goes through the point ( 4 , 5 ) and is parallel to the line 3 x + 4 y = 3 can be written in the form y = m x + b

Where M is?

Where B is?

Answer 1

Hello Grace,

Let's put the given equation into slope-intercept form first.

3x + 4y =3

→ 4y = -3x +3

→ y = (-3/4)x + 3/4

So the slope of the given equation is -3/4. Since we want a line that is parallel, we want to use the same slope with the coordinate (4,5).

From here, there are two options.

(I) Start with Slope-Intercept Form

(II) Start with Point-Slope Form, and turn into Slope-Intercept Form

Depending on where you are in the class, you may not have seen the second option, but just in case...

Option (I):

y = mx + b

→ 5 = (-3/4)(4) + b

→ 5 = -3 + b

→ b = 8

→ y = (-3/4)x + 8.

Option (II)

y - y₁ = m(x₁-x)

y - 5 = (-3/4)(x - 4)

→ y - 5 = (-3/4)x + 3

→ y = (-3/4)x + 8.

The answer is the same either way.

Thank you for posting the question. Have a great day!

Michael

Answer 2