A line passes through the origin and the point (1, 3) . Another line passes through the points (-3,1) and (1, - 7) What is the point intersection?

Answer 1

First, we find the equation of the lines.

Line that passes through the origin (0,0) and (1,3):

slope m = (3 - 0) / (1 - 0)

m = 3 / 1

m = 3

y - 3 = 3 (x - 1)

y - 3 = 3x - 3

y = 3x - 3 + 3

y = 3x

Equation of the line that passes through (-3,1) and (1,-7):

slope m = (-7 - 1) / (1 - (-3))

m = (-7 - 1) / (1 + 3)

m = -8 / 4

m = -2

y - (-7) = -2 (x - 1)

y + 7 = -2x + 2

y = -2x + 2 -7

y = -2x - 5

Finally, we find the point of intersection of both lines. At this point, the x and y coordinates are equal for both lines. So, to find those x and y coordinates we will set both lines equal to each other:

3x = -2x - 5

3x + 2x = -5

5x = -5

x = -5 / 5

x = -1

y = 3x

y = 3 (-1)

y = -3

Point of intersection: (-1, -3)

Answer 2

First, find the equation of both lines.

First line:

m=(y2-y1)/(x2-x1) = (3-0)/(3-1) = 3

(y-y1)=m(x-x1) Plug in the point and slope

(y-3)=3(x-1) Distribute

y-3=3x-3 Add 3 to both sides

y=3x

Second Line:

m=(y2-y1)/(x2-x1) = (-7-1)/(1-(-3)) = -8/4 = -2

(y-y1)=m(x-x1) Plug in the point and slope

(y-(-7))=-2(x-1) Distribute

y+7=-2x+2 Subtract 7 from both sides

y=-2x-5

Since both are in the form y= you can set the equations equal to each other

3x=-2x-5 Add 2x to both sides

5x=-5 Divide both sides by 5

x=-1

Plug into either equation to solve for y

y=3x

y=3(-1)

y=-3

The point is (-1,-3)