Question

How do you write an equation in slope intercept form given (5,7), (-3,11)?

Answer 1

`y=-12x+9 1/2`

Explanation:

Step 1: Write in slope-point form

`color(white)("XXX")`Step 1a: Determine the slope
`color(white)("XXX")color(green)m=(Deltay)/(Deltax)=(11-7)/(-3-5)=4/(-8)=color(green)(-1/2)`

`color(white)("XXX")`Step 1b: Use one of the given points to write in slope-point form:
`color(white)("XXX")y-7=-1/2(x-5)`

Step 2: Convert into slope-intercept form:
`color(white)("XXX")`Note the slope-intercept form is
`color(white)("XXXXXX")y=color(green)(m)x+color(blue)b`
`color(white)("XXX")`for a line with slope `color(green)(m)` and y-intercept `color(blue)(b)`

`color(white)("XXX")y=color(green)(-1/2)x+5/2+7`

`color(white)("XXX")y=color(green)(-1/2)x+color(blue)(19/2)`

Here is the graph of `y=-1/2x+19/2` with the given points for verification purposes: