Question

Question #487ba

Answer 1

`"slope "=3/2" and y-intercept "=-4`

Explanation:

The equation of a line in `color(blue)"slope-intercept form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=mx+b)color(white)(2/2)|)))`
where m represents the slope and b, the y-intercept.

`"Rearrange " 3x-2y=8" into this form"`

subtract 3x from both sides.

`cancel(3x)cancel(-3x)-2y=-3x+8`

`rArr-2y=-3x+8`

`"divide ALL terms by "-2`

`(cancel(-2) y)/cancel(-2)=-3/(-2)x+8/(-2)`

`rArry=3/2x-4larrcolor(red)" in slope-intercept form"`

`rArr"slope "=m=3/2" and y-intercept "=b=-4`

To graph the line using slope and y-intercept.

`• " Plot the point "(0,-4)larrcolor(red)"from y-intercept"`

`• m=3/2=("change in y")/("change in x")`

`rArr(0+2,-4+3)to(2,-1)larrcolor(red)" second point"`

`"A third point is useful when graphing a line"`

`"Repeat the process"`

`rArr(2+2,-1+3)to(4,2)larrcolor(red)" third point"`

`"Plot all 3 points and draw a straight line through them"`
graph{3/2x-4 [-11.25, 11.25, -5.62, 5.62]}