Question

Given `y+3=-2/3(x-3)` what is the slope and point on the graph?

Answer 1

`"slope"=-2/3, "point is" (0,-1)`

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 the given equation into this form.

distribute bracket on right side.

`rArry+3=-2/3x+2`

subtract 3 from both sides.

`rArry=-2/3x-1`

`rArrm=-2/3" and " b=-1`

y-intercept = - 1 which is the coordinate point (0 ,-1)

To obtain any coordinate point on the line, select values for x and substitute them into the equation for corresponding value of y.

`x=3rArry=(-2/3xx3)-1=-2-1=-3`

`rArr(3,-3)" is also a point on the line"`
graph{-2/3x-1 [-10, 10, -5, 5]}