If the slope is -2 and point A is (2,4) what would point B be?
Any other point of the line: y = -2x + 8
So what would the point of point B be?
There are actually infinite number of possible point B here, because if point A and point B lie on a line with a slope of -2, then two different points on that line have can be connected with a line of slope equal to -2. (I hope that's clear ^^;)
But just to show how to get one point on the line, we use here the formula for slope:
m = (y2 - y1)/(x2 - x1)
where m is the slope, and (x1,y1) and (x2,y2) are points on the line.
Substituting,
-2 = (y2 - 4)/(x2 - 2)
-2/1 = (y2 - 4)/(x2 - 2)
Equating numerators and denominators,
y2 - 4 = -2
y2 = -2 + 4
y2 = 2
x2 - 2 = 1
x2 = 1 + 2
x2 = 3
Thus, point B can be (3,2).
If however, the slope is rewritten as 4/(-2), which is still equal to -2, equating,
y2 - 4 = 4
y2 = 8
x2 - 2 = -2
x2 = 0
Thus, point B can also be (0,8), and there are infinite solutions.
Hope this helps :)
To find the coordinates of point B, we need to use the given slope and the coordinates of point A. The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. In this case, we have the slope (m = -2) and the coordinates of point A (x₁ = 2, y₁ = 4).
Step 1: Write down the equation using point-slope form.
y - y₁ = m(x - x₁)
Substitute the values:
y - 4 = -2(x - 2)
Step 2: Simplify the equation.
y - 4 = -2x + 4
Step 3: Solve for y by isolating it on one side.
y = -2x + 4 + 4
y = -2x + 8
Now, we have the equation in slope-intercept form.
Step 4: Substitute the value of x into the equation.
Let's consider any value of x, for instance, x = 0.
y = -2(0) + 8
y = 0 + 8
y = 8
So, when x = 0, y = 8. Thus, point B would be (0, 8)