Question

Write the equation of a line in slope-intercept form passing through (3, 5) and (2, 9)

Is it y=-4x+6 or y=-4x+17?
I think it's the first one, but I'm not sure.

Answer 1

\(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ 3}}\quad ,&{\color{blue}{ 5}})\quad &({\color{red}{ 2}}\quad ,&{\color{blue}{ 9}})
\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 2

what did you get for the slope?

Answer 3

I need slope intercept form not point slope. The slope is -4

Answer 4

ok so \(\bf \bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ 3}}\quad ,&{\color{blue}{ 5}})\quad &({\color{red}{ 2}}\quad ,&{\color{blue}{ 9}})
\end{array}
\\\quad \\

slope = {\color{green}{ m}}= -4
\\ \quad \\

y-{\color{blue}{ 5}}={\color{green}{ -4}}(x-{\color{red}{ 3}})\\
\qquad \uparrow\\
\textit{point-slope form}\)

by solving for "y", that'd give you more or less the slope-intercept form
we use the point-slope form only just to insert the values obtained

Answer 5

\(\bf y-5=-4(x-3)\implies y-5=-4x+12\implies y=-4x+12+5\)

Answer 6

so the slope-intercept form is \(\bf y=-4x+17\)

Answer 7

you can also plug the equations into a graphing calculator.. if you haave one. i did that and got the second equation for the correct answer

Answer 8

Really? Ok thanks