Aline goes through the points (8,9) and (-2,4). what is the slope of the line? (show your work) write the equation of the line in point-slope form. (show your work) write the equation of the line in slope-intercept form. (show your work)

Slope

The slope of the line between two points (x1, y1) and (x2, y2) is ...

... m = (y2 -y1)/(x2 -x1)

For your given points, the slope is

... m = (4 -9)/(-2 -8) = -5/-10

... m = 1/2

Equation

The point-slope form of the equation for a line can be written ...

... y = m(x -h) +k . . . . for a line of slope m through point (h, k)

Using the first point given and the slope just calculated, the equation for the line can be written ...

... y = (1/2)(x -8) +9

... y = (1/2)x -4 +9 . . . . eliminate parentheses; next, collect terms

... y = 1/2x +5

she will sew have sewn five dresses   and be 1/3 done with the sixth one in an hour.

step-by-step explanation:

3/4 of an hour=45 mins

lucy makes 1 dress per 11.25 minutes

45 mins+11.25 mins=56.25 mins

60 mins- 56.25 mins=3.75 mins

3.75 mins is 1/3 of of 11.25 mins

therefore she the other 1/3 would be part of the hour and she will have sewn 5 dresses and begun the sixth.

contact me if you have any questions you are welcome.