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A line has a slope of 1/3 and passes through the point (12, 16) . What is its equation in slope -intercept form?

User Douglas Reid
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1 Answer

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Answer: y = (1/3) * x + 4

The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope of the line and b is the y-intercept, the point where the line crosses the y-axis. In this case, we know that the slope of the line is 1/3 and that it passes through the point (12, 16), so we can plug these values into the equation to find the y-intercept.

To do this, we first need to rewrite the point (12, 16) in the form (x, y), where x and y are the coordinates of the point. We can then substitute these values into the equation y = mx + b to find the y-intercept. This gives us the following equation:

16 = (1/3) * 12 + b

We can then solve for b by multiplying both sides of the equation by 3 and then subtracting 36 from both sides:

48 = 3 * 12 + 3b

48 = 36 + 3b

12 = 3b

Therefore, the y-intercept of the line is 12/3 = 4.

Finally, we can use the values of the slope and y-intercept to write the equation of the line in slope-intercept form. This gives us the following equation:

y = (1/3) * x + 4

This is the equation of the line with a slope of 1/3 that passes through the point (12, 16).

User Igor Camilo
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