y=4x+17
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
[tex]\begin{gathered} slope=\frac{change\text{ in y }}{change\text{ in x}}=\frac{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}[/tex]
so
pick up 2 points from the the line and let
[tex]\begin{gathered} P1(0,10) \\ P2(10,50) \end{gathered}[/tex]
replace and evaluate
[tex]\begin{gathered} slope=\frac{change\text{\imaginaryI ny}}{change\text{\imaginaryI nx}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ slope=\frac{50-10}{10-0}=\frac{40}{10}=4 \end{gathered}[/tex]
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
[tex]\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}[/tex]
so
a)let
[tex]\begin{gathered} P1(2,25) \\ sloipe=4 \end{gathered}[/tex]
b) now ,replace and solve for y
[tex]\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}[/tex]
so, the answer is
y=4x+17
I
