Question

Find the equation of the line that passes between the points (-2,4) and (6,0).

i found that the slope is -1/2.

I know i have to st it up as
y-y1=m(x-x1)
but idk how to set it up.

Answer 1

y-y1=m(x-x1)

replace y1 with 4 and x1 with -2 (from -2,4)
replace m with -1/2

Answer 2

do exactly what you wrote

Answer 3

though using (6,0) looks easier (rather than -2,4)

Answer 4

First find the gradient: the formula for this is (change in y) divided by (change in x).
The change in y values is -4 (from 4 to 0) and the change in x is 8 (from -2 to 6).
So the gradient is \[\frac{ -4 }{ 8 } =-\frac{ 1 }{ 2 }\]

Now put this gradient in the standard equation of a line: y=mx+c, where m is the gradient and c is the y intercept.
So we have \[y=-\frac{ 1 }{ 2 }x + c\].
To find the y intercept (c), just put one of your points in. If we choose (6,0) then we have x=6 and y = 0, which gives us \[0=-\frac{ 1 }{ 2 } \times 6 + c\].
Simplify to 0=-3 + c and rearrange to c=3.
So the equation of the line is \[y=\frac{ -1 }{ 2 } x + 3\].

I know this is a different method to the one you were using but it can't hurt to know more than one way to solve a problem :)

Answer 5

\(\color{red}{m=-\frac{1}{2}}\)
\[\color{blue}{x_1=6}\]\[\color{green}{y_1=0}\]
\[y-\color{green}{y_1}=\color{red}{m}(x-\color{blue}{x_1})\]

Answer 6

\[y-\color{green}{0}=\color{red}{-\frac{1}{2}}(x-\color{blue}{6})\]

Answer 7

so the answer is y=-1/2x+3?

Answer 8

Yep

Answer 9

yes, in slope-intercept form

Answer 10

if we try the other point (-2,4) it should work:

4?= (-1/2)* -2 +3
4= 1+3
yes it worked.