Question

Indicate in standard form the equation of the line passing through the given points.

E(-2, 2), F(5, 1)

Answer 1

Metals for anyone who can help me

Answer 2

Drawing out the question will help a lot

Answer 3

the gradient (steepness) of the line can be calculated by dividing the change in y co-ordinate by the change in x co-ordinate
\[gardient = \frac{ \Delta y }{ \Delta x }\]

Answer 4

so gradient = -1/7

Answer 5

since \[gradient =\frac{ 1-2 }{ 5- (-2) }\]\[gradient = \frac{ -1 }{ 7 }\]

Answer 6

im writing all of this down in my notebook

Answer 7

so now we can use the formula
\[y-y1=m(x-x1)\] (where y1 and x1 are the y and x co-ordinate of the same point)
\[y-1=\frac{ -1 }{ 7 } (x-5)\] (i am using the co-ordinate (5,1))

Answer 8

rearranging the equation gives us
\[y-1 = \frac{ -x }{ 7 } +\frac{ 5 }{ 7 }\]

Answer 9

since 1 can be written as 7/7, we can replace 1 by 7/7

Answer 10

\[y-\frac{ 7 }{ 7 } = \frac{ -x }{ 7 } + \frac{ 5 }{ 7 }\]\[y=\frac{ -x }{ 7 } + \frac{ 5 }{ 7 } + \frac{ 7 }{ 7 }\]\[y=\frac{ -x }{ 7 }+\frac{ 12 }{ 7 }\]

Answer 11

and that is it...

Answer 12

the standard form of an equation of a straight line is
y=mx+c
where y and x are variable
m=gradient (-1/7 in our case)
c=y-intercept (12/7 in our case)

Answer 13

so how would you write that in standard form

Answer 14

that is the standard form... y=mx+c

Answer 15

y=(-1/7)x + (12/7)

Answer 16

it will not allow me to put that in my answer box

Answer 17

what does your answer box look like?

Answer 18

try 7y = -x + 12

Answer 19

box box box y= box box box box box

Answer 20

y= is given

Answer 21

try 7y = -x +12

Answer 22

yep thank you so much for the help

Answer 23

okay... have a nice day