Question

a line slope -4.5 passes through the point (6, -4). Use the definition of slope to find another point on the same line

Answer 1

The formula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

We have the point (6, -4) and the slope -4.5.

Substitute:

`(-4-y_1)/(6-x_1)=-4.5\\\\(-4-y_1)/(6-x_1)=(-45)/(10)\\\\(-4-y_1)/(6-x_1)=(-9)/(2)\qquad\text{cross multiply}\\\\2(-4-y_1)=-9(6-x_1)\qquad\text{use distributive property}\\\\(2)(-4)+(2)(-y_1)=(-9)(6)+(-9)(-x_1)\\\\-8-2y_1=-54+9x_1\qquad\text{add 8 to both sides}\\\\-2y_1=9x_1-46\qquad\text{divide both sides by (-2)}\\\\y_1=-4.5x_1+23`

Choice any value of x and calculate the value of y:

`for\ x_1=0\to y_1=-4.5(0)+23=0+23=23\to(0,\ 23)\\\\for\ x_1=2\to y_1=-4.5(2)+23=-9+23=14\to(2,\ 14)\\\\for\ x_1=4\to y_1=-4.5(4)+23=-18+23=5\to(4,\ 5)\\\vdots`

Answer 2

Answer: (8,-13)

The slope is -4.5 = -9/2 so that means we can move 9 units down and 2 units to the right to go from one point to another on this line.

slope = rise/run = -9/2 so we have rise = -9 and run = 2. A negative rise means we go down instead of up.

(x,y) = (6,-4) is the current point. If we move 9 units down, then we subtract 9 from the y coordinate y = -4 to get y-9 = -4-9 = -13. Moving 2 units to the right has us add 2 to the x coordinate x = 6 to get x+2 = 6+2 = 8

We start at (6,-4) and end up at (8,-13). This process can be repeated forever to get as many points as you want, so this point is not the only possible answer.