## Alberta Free Tutoring And Homework Help For Math 10C

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### The questions is "A linear relation passes through the points (-40,19) and (24,91). Determine equations for the relation in slope intercept form, general form and slope point form." I am having trouble convering the slope intercept form which is y=1.125(x)+64 for the points provided, to general form. Ax+By+C=0 is general form and because the slope is 1.125 or 1.1/8 i am having trouble converting so that the numbers are whole.

4 years ago

The slope of this line is 1.125. To transition from slope intercept form to general form, you just need to move the y to the other side of the equal sign using subtraction.

y = 1.125x + 64

-y     -y

________________

0 = 1.125x - y + 64

The numbers in front of the variables (1.125, -1) and the constant (64) do not need to be whole numbers.

4 years ago

Given Point Slope Form is, y = 1.125x + 64

and we have a slope = 1.125 from the above point slope form

*1st step:*

Convert the slope=1.125  from Decimal to Fraction form

1.125 = 1125/1000, simply this fraction and you will get 9/8

*2nd Step:*

you can write the point slope form as

y = 9/8x + 64, [and from step 1 you already know that 1.125 = 9/8]

so now multiply the above equation by 8

8y = 9/8x(8) + 64(8)

8y = 9x + 512

*3rd Step:*

rearrange the equation so that we can get the standard form

9x - 8y + 512 = 0 which is the general form Ax + By + C = 0

All the numbers are whole numbers :) hope it works!

4 years ago

Given two points on the line, (-40,19) and (24,91) we get the slope from rise over run.

$\frac{rise}{run}=\frac{91-19}{24-\left(-40\right)}=\frac{72}{64}=\frac{9}{8}=1.125=m$riserun =911924(40) =7264 =98 =1.125=m

So now for Slope Intercept form,  $y=mx+b$y=mx+b

we have  $m=\frac{9}{8}=1.125$m=98 =1.125 but we need to find the y-intercept b.

To do this we need to use one of the points we've been given. Either one will do so lets use (-40,19)

What this tells us is when  $x=-40$x=40 ,  $y=19$y=19, so lets plug that in to the general slope-intercept

$19=\frac{9}{8}\left(-40\right)+b$19=98 (40)+b

now solving for b we get

$19=-45+b$19=45+b

$b=64$b=64

thus our Slope Intercept form is

$y=\frac{9}{8}x+64$y=98 x+64

To get General Form  $Ax+By+C=0$Ax+By+C=0

we simply move everything to one side of the equation, giving us

$-\frac{9}{8}x+y-64=0$98 x+y64=0

and we can pull our A,B, and C values from this

$A=-\frac{9}{8}$A=98

$B=1$B=1

$C=-64$C=64

I prefer to leave slopes in fractional form rather than decimals because I can do more with that information than I can with decimals like 1.125.

For instance, to get the Slope Point form

$\left(y-k\right)=m\left(x-h\right)$(yk)=m(xh)

we need a point on the line, and maybe we don't want to use the ones given.

starting at the y-intercept, (0,64) (from the slope intercept form)

we can rise by 9 and run by 8, giving us another point on the line at (8,73)

(not easily found using 1.125)

this works for our (h,k) point and gives us the Slope Point form

$\left(y-73\right)=\frac{9}{8}\left(x-8\right)$(y73)=98 (x8)