Question

The equation of the graphed line in point-slope form is?, and it’s equation in slope-intercept form is?

Answer 1

Slope

`m=-(3)/(5)`

point-slope form

`y=-(3)/(5)(x-3)`

slope-intersection form

`y=-(3)/(5)x+1.8`

Explanation:

The equation of a line in the point-slope form has the following formula:

`y-y_0 = m (x-x_0)`

Where m is the slope and
`(x_0, y_0)` is a point belonging to the line.

The equation of a line in the slope-intersection form has the following formula:

`y = mx + b`

Where b is the intersection of the line with the y axis.

To calculate the slope of the line knowing 2 points we use the following formula:

`m=(y_1-y_0)/(x_1-x_0)`

In this case:

`x_0 =3\\y_0=0\\x_1=-2\\y_1=3`

So

`m=(3-0)/(-2-3)`

`m=-(3)/(5)`

So the equation of a line in the point-slope form

`y-0 =-(3)/(5)(x-3)`

`y=-(3)/(5)(x-3)`

The equation of a line in the slope-intersection form is:

`y-0=-(3)/(5)(x-3)`

`y=-(3)/(5)(x-3)`

`y=-(3)/(5)x+(9)/(5)`

`y=-(3)/(5)x+1.8`

with
`b=1.8`

Answer 2

Point-slope form:

`y - 3 = -(3)/(5) (x + 2)`

Slope-intercept form:

`y= -(3)/(5) x + (9)/(5)`

EXPLANATION

The graphed line passes through

`(-2,3) \: \: and \: \: (3,0)`

The slope of this line is determined using

`m = (y_2-y_1)/(x_2-x_1)`

We substitute the points to get;

`m = (0 - 3)/(3 - - 2)`

`m = -(3)/(5)`

The point-slope formula is:

`y-y_1 = m(x - x_1)`

Substitute the first point and slope to get:

`y - 3 = -(3)/(5) (x - - 2)`

`y - 3 = -(3)/(5) (x + 2)`

To find the slope-intercept form, we expand to get:

`y= -(3)/(5) x - (6)/(5) + 3`

`y= -(3)/(5) x + (9)/(5)`