Any ideass on how to do this?

Question

A line with a slope of 4 and goes through the point (9,8)

point slope:__

slope-intercept:____

standard form:___

and then i have another problem that gives me 2 points

like (-2,-7) and (-6,-3)

but no slope..how do i find the point slope, slope intercept and standard form of that one??

Answer 1

Point slope form is really easy.  Plug in the known slope and point into the equation (y-y1)=m*(x-x1)

(y-8)=4*(x-9)

Slope intercept form is y=mx+b.  

Plug in the known x,y and the known slope:

8=4*9+b

8=36+b

b=-28

y=4x-28

To get this in standard form, subtract 4x from both sides:

-4x+y=-28

Then multiply by -1 to give x a positive coefficient

4x-y=28

When you have 2 points, it's easy to calculate the slope.  Take the difference of the y's divided by the difference of the x's.

Difference of the y's: (-7-(-3)) or -7+3 or -4

Difference of the x's: (-2-(-6) or -2+6 or 4

Slope = -4/4 or -1

To find the point-slope form, plug in the known point and the (now-known) slope:

(y+7)=(-1)*(x+2)

To find the slope- intercept form, plug in the known x, y and slope to find the intercept:

y=(-1)*x+b

-7=(-1)*(-2)+b

-7=2+b

b=-9

y=(-1)*x+9

And to find the standard form, just take that slope intercept form and rearrange.  Add x to both sides:

x+y=9

And you're done.

_/