Write the slope-intercept form of the line passing through (–8, –5) and (4, 4).

Step-by-step explanation:

We can find the slope through two points.

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

m = (4 - -5)/(4 - -8)

m = 9/12 = 3/4

The slope of the line is 3/4.

Slope-intercept form of a line is y=mx+b. Where m is the slope and b is the y-intercept.

y = 3/4x + b

A point on the line is (4, 4). x = 4 and y =4.

4 = 3/4(4) + b

4 = 3 + b

b = 1

The y-intercept is 1.

Step-by-step explanation:

Finding the slope (m) first:

Given the coordinates (-8 , -5) and ( 4 , 4 )

Slope =

Slope =

Slope =

Slope =

Slope = m =

Finding y - intercept (b) :

Taking a coordinate say (4,4)

And putting it in slope intercept form along with b

y = mx+b

Where y = 4 , m = 3/4 and x = 4

4 = (3/4)(4) + b

4 = 3+b

4-3 = b

1 = b

So,

b = 1

Putting m and b now in slope-intercept equation:

y = mx+b

To affirm that it exists a solution to the equation f(x) = g(x) between x =3 and x =4 you should state the continuity of the functions.

1) Being f(x) a linear function means it is well defined between the points x = 3 and x =4 and you can conclude that it is a decreasing continuos function (decreasing because f(4) < f(3).

2) Being g(x) a ratonal functiion means that it is the ratio of two polynomials, g(x) = p(x) / m(x).Then, g(x) is continuous in the range [3,4] if and only if m(x) ≠ 0in the same range.

3) Given that you do not know whether m(x) meets that condition, you cannot conclude whether theres is a solution or not to f(x) = g(x).