What is the y-intercept of the equation of the line that is perpendicular to the line y = 3/5 x + 10 and passes through the poin
t (15, –5)?
The equation of the line in slope-intercept form is y = -5/3x+ ? ____
The equation of the line in slope-intercept form is y = -5/3x+ ? ____
1 answer:
The slope of the given line is the coefficient of x, 3/5. The slope of the perpendicular line is the negative reciprocal of that:
... m = -1/(3/5) = -5/3
The point-slope form of the equation of a line can be written as
... y = m(x -h) +k . . . . .for slope m and point (h, k)
Using the values we are given for the perpendicular line, its equation is
... y = (-5/3)(x -15) -5
Simplifying gives
... y = (-5/3)x +20
The y-intercept of the perpendicular line is 20.
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This is rather a sneaky question. You don't know exactly what numbers you can use and what numbers not.
For example, are you allowed to use x = - 3. The answer is yes
f(-3) = 2*7^(-3) = 2/7^3 = 2/147.
How about 0? If there is going to be a problem, zero is usually the number that causes the problem.
f(0) = 2*7^(0) = 2 * 1 = 2 and in this case 0 is just fine.
How about positive numbers? No they are all good.
So the range is -∞ < y < ∞
