Question

In the xy-plane, line t has equation y=1/4x+3, and line m has equation y=1/2x+b, If the lines intersect at the point with coordinates (t,11/2), what is the value of b.

Answer 1

substitute y=11/2 into the equation

Answer 2

@ganeshie8

Answer 3

\[y=\frac{ x }{ 4 }+3\]

Answer 4

\[\frac{ 11 }{ 2 }=\frac{ x }{ 4 }+3\]

Answer 5

@AaronAndyson

Answer 6

Multiply 2 on both sides

Answer 7

so you're basically solving for x after that?

Answer 8

\[2\times \frac{ 11 }{ 2 }=2(\frac{ x }{ 4 }+3)\]

Answer 9

wait no

Answer 10

sorry continue

Answer 11

\[11=\frac{ x }{ 2 }+6\]

Answer 12

subtract 6 on both sides

Answer 13

\[5=\frac{ x }{ 2 }\]

Answer 14

Then,multipy 2 on both sides

Answer 15

\[x=5\times2\]\[x=10\]

Answer 16

substitute x=10 and y=11/2 into the second equation in oder to find the value of b

Answer 17

\[y=\frac{ x }{ 2 }+b\]

Answer 18

\[\frac{ 11 }{ 2 }=\frac{ 10 }{ 2 }+b\]

Answer 19

\[\frac{ 11 }{ 2 }=5+b\]

Answer 20

Multiply 2 on both sides

Answer 21

\[2\times \frac{ 11 }{ 2 }=2(5+b)\]

Answer 22

\[11=10+2b\]

Answer 23

subtract 10 on both sides

Answer 24

\[11-10=2b\]

Answer 25

\[1=2b\]

Answer 26

divide 2 on both sides

Answer 27

\[b=?\]solve it @Mhm120