Question

Write the equation of a line passing through the points (3,-4) and (2,6) for fan and medal!

Answer 1

@mathstudent55

Answer 2

@mathmale

Answer 3

@Hero

Answer 4

@jdoe0001

Answer 5

@zzr0ck3r

Answer 6

Do you know how to find the slope given two points?

Answer 7

yep!

Answer 8

Okay, then do that first.

Answer 9

-2

Answer 10

is the slope

Answer 11

so what do i do next!

Answer 12

\(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ 3}}\quad ,&{\color{blue}{ -4}})\quad &({\color{red}{ 2}}\quad ,&{\color{blue}{ 6}})
\end{array}
\\\quad \\

slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies \cfrac{{\color{blue}{ y_2}}-{\color{blue}{ y_1}}}{{\color{red}{ x_2}}-{\color{red}{ x_1}}}
\\ \quad \\

y-{\color{blue}{ y_1}}={\color{green}{ m}}(x-{\color{red}{ x_1}})\qquad \textit{plug in the values and solve for "y"}\\
\qquad \uparrow\\
\textit{point-slope form}\)

Answer 13

so y=-2x+b

Answer 14

No. The point-slope equation is y-y1=m(x-x1)
Choose any of the points that you listed in the original equation. I will choose 3,-4.
y+4=-2(x-3)
y+4=-2x+6
-4 -4
y=-2x+2

Answer 15

Actually you did your slope wrong.

Answer 16

\[\frac{ y2-y1 }{ x2-x1 } = \frac{ 6+4 }{ 2-3 }=\frac{ 10 }{ -1 }=-10\]
NOW we can use the original points and plug them into the point-slope equation.
y+4=-10(x-3)
y+4=-10x+30
-4 -4
y=-10x+26

Using this equation we can double check our work with the other point, 2,6.
6=-10(2)+26
6=-20+26
6=6
So yes, that is the proper equation.