So if point A is (2,4) and point B is (3,2) and slope is -2 how would I find the x and y intercepts?
(y-4)/(x-2) = (2-4)/(3-2)
y-4 = -2(x-2)
y = -2x+8
if x=0, y=8
if y=0, x=4
so, the intercepts are (0,8) and (4,0)
I'm hoping you can figure out which is which
Is this the continuation of your question? :)
In the previous question, we know the slope is -2, and therefore we use the point-slope formula to get the equation:
y - y1 = m(x - x1)
We only need the slope and one point to get the equation. Let's use the point(2,4). Substituting,
y - 4 = -2(x - 2)
y - 4 = -2x + 4
y = -2x + 8
To get the x-intercept, let y = 0 and solve for x:
0 = -2x + 8
2x = 8
x = 4
x-intercept is at (4,0).
To get y-intercept, let x = 0 and solve for y:
y = -2(0) + 8
y = 8
y-intercept is at (0,8).
Hope this helps :)
Okay!! So would y=-2x+8 be the equation?
Yes. :) The equation containing (2,4) with slope equal to -2 is y = -2x + 8.
So now I then have to put it in a equation of line parallel thorough (-2,0). How would I do that?
Then after that I would have to put equation of line perpendicular through y-intercept. How would I do that too?
Thanks so much for help me I really don't understand this!!
you know the parallel line also has slope -2, so using the point-slope form, that is
(y-0) = -2(x-2)
.......................
the perpendicular line has slope -1/(-2) = 1/2
Figure the y-intercept and you again have a point and a slope.
To find the x-intercept, we need to determine the point at which the line crosses the x-axis. At the x-intercept, the value of y is zero.
Given the slope-intercept form equation, y = mx + b, where m represents the slope and b represents the y-intercept, we can substitute the given slope -2 into the equation as follows:
0 = -2x + b
To find the value of b, we need to use one of the given points (2,4) or (3,2).
Using point A (2,4):
4 = -2(2) + b
4 = -4 + b
b = 8
Thus, the equation of the line becomes:
y = -2x + 8
Now, to find the x-intercept, we set y to zero:
0 = -2x + 8
Solving for x:
2x = 8
x = 4
Therefore, the x-intercept of the line is 4.
To find the y-intercept, we need to determine the point at which the line crosses the y-axis. At the y-intercept, the value of x is zero.
Substituting x = 0 into the equation y = -2x + 8:
y = -2(0) + 8
y = 8
Thus, the y-intercept of the line is 8.