Answer:
The point-slope equation for a line that goes through the point (4, 1/3) with a slope of 3/4 is:
Choice B: [tex]\displaystyle y - \frac{1}{3} = \frac{3}{4}(x - 4)[/tex].
Step-by-step explanation:
This question gives
- a point on the line,
- the slope (a.k.a. gradient) of the line.
Consider the point-slope form of the equation of a line in a cartesian plane:
[tex]y - y_0 = m (x - x_0)[/tex],
where
- [tex]x_0[/tex] and [tex]y_0[/tex] are the coordinates of the given point. The point on the line is [tex](x_0, y_0)[/tex].
- [tex]m[/tex] is the slope of the line.
For this line:
- The given point is [tex]\displaystyle (4,\; \frac{1}{3})[/tex] where [tex]x_0 = 4[/tex] and [tex]\displaystyle y_0 = \frac{1}{3}[/tex].
- The slope of the line: [tex]\displaystyle m = \frac{3}{4}[/tex].
The point-slope equation of this line will be:
[tex]\displaystyle y - \frac{1}{3} = \frac{3}{4}(x - 4)[/tex].
