Write the equation of a line with a slope of 3 and passes through the point (-1,-8). Show steps please

y=3x-5

Step-by-step explanation:

We are given a point and a slope, so we can use the point-slope formula.

where m is the slope and (x₁, y₁) is the point.

The slope is 3 and the point given is (-1,-8). Therefore,

Substitute the values into the formula.

Simplify the signs. Two negative signs become a positive sign.

Distribute the 3. Multiply each term inside the parentheses by 3.

We want to find the equation in slope-intercept form: y=mx+b. Therefore, we must isolate y. 8 is being added to y. The inverse of addition is subtraction. Subtract 8 from both sides.

The equation of the line is y=3x-5 ⇒ m= 3, b= -5

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

80 the answer is 80

step-by-step explanation: