Coordinate geometry?

Question

A line passes through points (-2,-1) and (4,3). Where does the line intersect the x-axis and the y-axis?

Answer 1

First write the equation for the line by substituting (-2,-1) and (4,3) into the equation. (y-y1)/(x-x1) = (y2-y1)/(x2-x1). Where y1 is -1 and x1 is -2, y2 is 3 and x2 is 4.

In this case this (y- -1)/(x- -2) = (3- -1)/(4- -2)
=(y+1)/(x+2) = 4/6
= 6y+6 = 4x+8
now put this equation in the y=mx+c form
= y = 2/3x + 1/3
This means that the y intercept is 1/3 (found by substituting x=0) and the x is ( found when y=0) -1/2

Answer 2

You can use the slope-intercept form of a line to determine its y intercept. The y intercept is the point where the line crosses the Y axis and so with the X intercept that is the point where the line crosses the x axis. Now the slope intercept form is like this:

y = mx + b

Where:
b is the y intercept and m is the slope of the line.
The formula for the slope is:

Slope = m = y2-y1 / x2-x1

So we will have:

3 - (-1) / 4 - (-2) = 3 + 1 / 4+2 = 4/6 = 2/3

Now we also have the slope-intercept form which goes like this:

y - y1 = m (x - x1)

Where (x1, y1) is a point on the line. You already have two points on the line so we will choose the first for example for x1 and y1 and we calculated the slope which is (2/3) now plug them into the above formula:

y - 3 = 2/3 * (x-4)
y-3 = 2/3x - 8/3
y = 2/3x - (8/3+3)
y = 2/3x - 17/3

Now that is the form of line in the y-intercept form where B (the y-intercept) is -17/3

That is the point where your line crosses the y axis. The x intercept is also 2/3. So your line crosses the y axis at -17/3 and the x axis at 2/3

Good luck.

Answer 3

If the line is y = Mx + B, you can substitute these two coordinates into the equation and form two equations with unknowns M and B. Solve them.

M is the slope and B is the intercept, where the line intercepts the x-axis. By setting y=0, x= -B/M, which is the coordinates for the y-axis intercept.

Answer 4

IN this problem we can use the formula.....
y-y,= (y,,-y,/x,,-x,)(x-x,)

so, we will substitute your given (-2,-1)&(4,3)

y-(-1)= (3-(-1) / 4-(-2)) (x-(-2))
y+1=(4/6)(x+2) or y+1=(2/3)(x+2)
3y+3=2x+4
then transpose.....

[-2x+3y=1]-1 is equal to 2x-3y=-1

To know the y-intercept substitute x with 0.
2(0)-3y=-1
-3y=-1 all over -3
so y=1/3

To know the x-intercept sustitute y with 0.
2x-3(0)=-1
2x=-1 all over 2
so x= -1/2

Therefore the line intersect at (1/3, -1/2)..

Answer 5

2 &4