how do you solve y=7;(2,4) ?

Question

how do you solve it?

Answer 1

(Assuming that this is for a linear equation)

So y = 7, and the line passes through the point (2,4).

Our coordinates will be (x₁,y₁) and (x₂,y₂).

(x1,y1)=(2,4)

(x2,y2)=(x,7)

Our steps: 

1. Solve for m.

2. Solve for x.

3. Solve for b.

4. Write y=mx+b equation.

5. Check for accuracy.

 

First, we set up our equations:

y=mx+b.

y-y1=m(x-x1)+b

 

Step 1: Solve for m.

y=mx+b, (2,4) (Remember that the slope won't change regardless of what b is.)

4=2m.

m=2.

 

Step 2: Solve for x

y-y₁=m(x-x₁)

7-4=2(x-2). 

3=2(x-2)

3/2=x-2

2+3/2=x

x=4/2+3/2

x=7/2.

 

Step 3: Solve for b.

y=mx+b, (7/2,7)

7=2(7/2)+b (Twos cancel out)

7-7=b

b=0.

 

Step 4: Write y=mx+b equation.

(x1,y1)=(2,4)
(x,y)=(7/2,7)

m=2

 

y-y1=m(x-x1)+b

7-4=2(7/2-4/2)+b (Substitute, 2=4/2)

3=2(3/2)+b (2s cancel, subtract 3.)

3-3=b

b=0

y=2x+0

y=2x. 

 

Step 5: Check for accuracy.

(x1,y1)=(2,4), m=2, b=0

y=mx+b

4=2(2) Yes

 

(x,y)=(7/2,7), m=2, b=0

7=2(7/2) Yes.

The answer is y=2x.