The slope is three times the y-intercept and through (-3,10). How do I know the equation?
Let the y-intercept be (0,k). Now you have two points, so the slope is
(10-k)/-3
We are told that the slope is 3k, so that makes m = k-10
The point-slope form for the line is now
y-10 = (k-10)(x+3)
P(-3, 10).
Y = mx + b,
m = 3b,
Y = (3b)x + b,
10 = (3b)(-3) + b,
b = -10/8 = - 5/4 = -1.25.
m = 3b = 3*(-1.25) = -3.75.
Eq: Y = -3.75x - 1.25.
well, duh.
Nice save, henry2
Thanks, oobleck.
To find the equation of a linear equation in the form of y = mx + b, where m represents the slope and b represents the y-intercept, you need to determine both the slope and the y-intercept.
Given that the slope is three times the y-intercept, we can write the equation as:
y = 3b * x + b
Next, we'll use the given point (-3, 10) to determine the values of b and m.
Step 1: Substitute the given x and y values into the equation:
10 = 3b * (-3) + b
Step 2: Simplify the equation:
10 = -9b + b
Step 3: Combine like terms:
10 = -8b
Step 4: Solve for b by dividing both sides of the equation by -8:
b = -10/8
b = -5/4
Now that we have the value of b, we can substitute it back into the equation to find m:
y = 3b * x + b
y = 3(-5/4) * x + (-5/4)
y = (-15/4)x - 5/4
Therefore, the equation of the line is y = (-15/4)x - 5/4.