Write an equation in point-slope form and slope-intercept form for each line.
the line passes through (4, 7), slope = 2

point slope: y-7=2(x-4

slope intercept: y=2x-1

Step-by-step explanation:

point slope form: y-y1=m(x-x1)

(4,7) and m=2

using all the info here is it in point slope form: y-7=2(x-4)

turning the point slope equation into slope intercept...

slope intercept form: y=mx+b

first simplify y-7=2(x-4) into y-7=2x-8

then add 7 to both sides...

which would be y=2x-1

and thats your answer!!

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

3

step-by-step explanation: