Question

Can I get some help ASAP please 15 points

Answer 1

The slope of the line is 3. In slope intercept form, it is y=3x+3 and in point slope form it is y-0=3(x+2)

Answer 2

a) slope =
`=(3)/(2)`

b)
`y=(3)/(2) x+3`

c) y-0=\frac{3}{2} (x+2)

Explanation:

Notice that there are two clear points that the line goes through (intersection with the axes): the point (-2,0) on the horizontal axis, and the point (0,3) on the vertical axis.

Part a)

For the slope of the line that goes through two points, use the given points as
`(x_1,y_1)=(-2,0)`,
`(x_2,y_2)=(0,3)` and the definition of slope:

`slope=(y_2-y_1)/(x_2-x_1) =(3-0)/(0-(-2)) =(3)/(2)`

Part b)

For the slope y-intercept part use the slope we just found, and for the y-intercept (b) use what you know from the graph, the point (0, 3):

`y=mx+b\\y=(3)/(2) x+b\\y=(3)/(2) x+3\\`

Part c)

For this part, use the slope that we found in part a), and also use either point you know belong to the line from our studies above, for example the point
`(x_1,y_1)=(-2,0)`.

Recall the general form of the slope-point form of a line:

`y-y_0=m(x-x_0)` where m is the slope (we then use 3/2 for this), and the values
`x_0` and
`y_0` and the x and y values of a point the line goes through [(-2,0) was our selected point]. so with replace
`x_0` with "-2" and
`y_0` with 0 in the general form:

`y-0=(3)/(2) (x-(-2))\\y-0=(3)/(2) (x+2)`