Question

What is an equation of the line parallel to the line on the graph that passes through (2,25)?

Answer 1

y=4x+17

Step-by-step explanation

Step 1

2 equations of lines are parallel if the slope is the same, so

a) find the slope of the graphed line

the slope of a line can by calculated by using

`\begin{gathered} slope=\frac{change\text{ in y }}{change\text{ in x}}=(y_2-y_1)/(x_2-x_1) \\ where \\ P1(x_1,y_1) \\ and \\ P2(x_2,y_2) \\ are\text{ 2 points from the line} \end{gathered}`

so

pick up 2 points from the the line and let

`\begin{gathered} P1(0,10) \\ P2(10,50) \end{gathered}`

replace and evaluate

`\begin{gathered} slope=\frac{change\text{\imaginaryI ny}}{change\text{\imaginaryI nx}}=(y_(2)-y_(1))/(x_(2)-x_(1)) \\ slope=(50-10)/(10-0)=(40)/(10)=4 \end{gathered}`

hence, the slope of the line is 4

Step 2

now, using the slope and a point we can find the equation of the line

use the point-slope formula, it says

`\begin{gathered} y-y_1=m(x-x_1) \\ where\text{ m is the slope} \\ (x_1,y_1)\text{ is a point from the line} \end{gathered}`

so

a)let

`\begin{gathered} P1(2,25) \\ sloipe=4 \end{gathered}`

b) now ,replace and solve for y

`\begin{gathered} y-y_(1)=m(x-x_(1)) \\ y-25=4(x-2) \\ y-25=4x-8 \\ add\text{ 25 in both sides} \\ y-25+25=4x-8+25 \\ y=4x+17 \end{gathered}`

so, the answer is

y=4x+17

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