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

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true