Question

(25 POINTS!!)What is the equation of the line that passes through the points (15,9) and (-2,9)?

Answer 1

$\text{d stands for distance between two points} \\d(A, B)=\sqrt{(\Delta{x})^2+(\Delta{y})^2} \\\text{or simply} \\d(A, B)=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\text{now put in the data} \\d(A, B)=\sqrt{(-2-15)^2+(9-9)^2} \\d(A, B)=\sqrt{(-17)^2} \\d(A, B)=\boxed{17}$

Answer 2

Let's use the point-slope formula...

y-y1=m(x-x1)

m is the slope.

y--9=7(x--2)

Subtracting a negative number is the same as adding a positive number...

y+9=7(x+2)

y+9=7x+14

Let's subtract 9 from both sides...

-9+y+9=7x+14-9

y=7x+5

The formula is now in the format of...

y=mx+b

This is known as slope-intercept.

m is the slope.

b is the y-intercept, the value of y when x=0.

Standard formula is...

Ax+By=C

Neither A nor B equal zero.

A is greater than zero.

y=7x+5

Let's move 7x to the left side of the equation.  It becomes negative.

-7x+y=5

Let's multiply both sides by -1 to render A greater than zero.

-1(-7x+y)=(5)(-1)

7x-y=-5

This is the equation in standard form.