The value of y varies directly with the value of x. When y = 24, x = 4. What is the value of x when y = 48?
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Answer:
Step-by-step explanation:
We are given that a line has a slope of -2/3 and passes through the point (0,6)
We want to write the equation of this line; there are 3 forms of the line that we can use:
- Slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept
- Standard form, which is ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be 0, and a cannot be negative
- Slope-point form, which is
, where m is the slope and
is a point
All though while writing the equation of the line in any of these ways is acceptable, the most common way is to write it in slope-intercept form, so let's do it that way.
As we are already given the slope, we can immediately substitute m with that value.
Replace m with -2/3:
y = -2/3x + b
Now we need to find b.
As the equation passes through the point (0, 6), we can use it to help solve for b.
Substitute 0 as x and 6 as y.
6 = -2/3(0) + b
Multiply
6 = 0 + b
Add
6 = b
Substitute 6 as b.
y = -2/3x + 6
Topic: finding the equation of the line
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