Question

Which equation represents a line that passes through (4,1/3 ) and has a slope of 3/4?

y – = (x – 4)
y – = (x – 4)
y – = 4(x – 3/4)
y – 4 = (x – 1/3)

Answer 1

For this case we have that by definition, the slope-intersection equation of a line is given by:

`y = mx + b`

Where:

m: It's the slope

b: It is the cut point with the y axis.

They tell us as data that:

`m = \frac {3} {4}`

Now the equation is:

`y = \frac {3} {4} x + b`

We substitute the point to find "b":

`(4, \frac {1} {3})`

`\frac {1} {3} = \frac {3} {4} (4) + b`

`b = \frac {1} {3} -3\\b = - \frac {8} {3}`

Finally the equation is:

`y = \frac {3} {4}x - \frac {8} {3}`

In point-slope form the equation is:

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

Answer:

`y = \frac {3} {4}x - \frac {8} {3}`

Answer 2

y - 1/3 = 3/4(x - 4)

Explanation:

We know that the general equation of a line is the following:

y - yo = m(x-xo), where 'm' represents the slope of the line, and (xo, yo) is any point that belongs to the line.

Then, the equation of the line that passes through (4, 1/3) and has a slope of 3/4 is: y - 1/3 = 3/4(x - 4)