Question

write an equation for the line in slope-intercept form passing through (2, 3) and (8, 2)

Answer 1

\(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ 2}}\quad ,&{\color{blue}{ 3}})\quad &({\color{red}{ 8}}\quad ,&{\color{blue}{ 2}})
\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

@jdoe0001 that looks nice in color
@hahaalgebra do you have any questions after following the above?

Answer 3

i cannot get the point slope form

Answer 4

I came out with -1/6

Answer 5

slope-intercept form y = m x + b
where m is the slope and b is the y-intercept

Answer 6

yes the slope is correct -1/6

Answer 7

so is it y-3=-1/6(x-2)

Answer 8

use one of the given points, plug the x, y and m then find b

Answer 9

yes you have it in point-slope form and the question ask for slope-intercept form so now just rearrange to y =

Answer 10

so I add 3 to both sides

Answer 11

yes you also need to expand the parenthesis

Answer 12

y = m x + b

Answer 13

i am lost
y = -1/6 + 10/3

Answer 14

you lost your x

Answer 15

oops y = -1/6x + 10/3

Answer 16

y-3=-1/6(x-2)
y - 3 = -1/6(x) -1/6(-2)
y = -1/6 x + 10/3

Answer 17

hint first check what format the answer should be in (standard, point-slope, or slope-intercept)
for this one requested slope-intercept so just plug with the given point to find b
of course you see you will get the same answer to put in point-slope and then rearrange

Answer 18

and you know the slope is the change in y / corresponding change in x

Answer 19

thank you for your help