Rewrite the following equation in slope-intercept form.7x − 15y = –18
2 answers:
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Use Hooke's law to find the spring constant. If it takes 8N to stretch the spring by 0.1m, then
I'm going to assume the spring is fixed to a ceiling, and that any stretching in the downward direction counts as movement in the positive direction. The spring's motion is then modeled by
where
is the position of the spring's free end as it moves up and down. Solving this is easy enough: the characteristic solution will be
Given that the spring is stretched to a length of 1m (a difference of 0.25m from its natural length), and is released with no external pushing or pulling, we have the two initial conditions
and 
.
So the spring's motion is dictated by the function
I'm going to assume the spring is fixed to a ceiling, and that any stretching in the downward direction counts as movement in the positive direction. The spring's motion is then modeled by
where
Given that the spring is stretched to a length of 1m (a difference of 0.25m from its natural length), and is released with no external pushing or pulling, we have the two initial conditions
So the spring's motion is dictated by the function
Given:
A table of values of a linear function.
To find:
The slope, y-intercept and equation of the function.
Solution:
Take any two points on the table.
Let the points are (-1, -3) and (0, -6).
Slope of the line:
m = -3
Slope of the function = -3
y-intercept of the function is the point where x = 0.
In the table y = -6 when x = 0
y-intercept = -6
Equation of a line:
y = mx + c
where m is the slope and c is the y-intercept
y = -3x + (-6)
y = -3x - 6
Equation of a function is y = -3x - 6.