Which equation represents a line that passes through (4, left-parenthesis 4, StartFraction one-third EndFraction right-parenthesis.) and has a slope of StartFraction 3 Over 4 EndFraction.?

Question

y – y minus StartFraction one-third EndFraction equals StartFraction 3 Over 4 EndFraction left-parenthesis x minus 4 right-parenthesis. = y minus StartFraction 3 Over 4 EndFraction equals StartFraction one-third EndFraction left-parenthesis x minus 4 right-parenthesis.(x – 4)
y – y minus StartFraction one-third EndFraction equals 4 left-parenthesis x minus StartFraction 3 Over 4 EndFraction right-parenthesis. = y minus StartFraction one-third EndFraction equals StartFraction 3 Over 4 EndFraction left-parenthesis x minus 4 right-parenthesis.(x – 4)
y – y minus StartFraction one-third EndFraction equals 4 left-parenthesis x minus StartFraction 3 Over 4 EndFraction right-parenthesis. = 4(x – )
y – 4 = y minus 4 equals StartFraction 3 Over 4 EndFraction left-parenthesis x minus StartFraction one-third EndFraction right-parenthesis.(x – )

Answer 1

To find the equation of a line that passes through the point \((4, \frac{1}{3})\) and has a slope of \(\frac{3}{4}\), we can use the point-slope form of the equation of a line:

\[ y - y_1 = m(x - x_1) \]

where \(m\) is the slope, and \((x_1, y_1)\) is the point through which the line passes.

In this case, \(m = \frac{3}{4}\), \(x_1 = 4\), and \(y_1 = \frac{1}{3}\). Now we substitute these values into the equation:

\[ y - \frac{1}{3} = \frac{3}{4}(x - 4) \]

This is the equation that represents the line that passes through the point \((4, \frac{1}{3})\) with a slope of \(\frac{3}{4}\).

So, the correct representation of the line is:

\[ y - \frac{1}{3} = \frac{3}{4}(x - 4) \]

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