Graph the line having a slope of $\frac{1}{3}$ and passes through $(4,3)$.

• A.
• B.
• C.
• D.

Answer: (B)

Verified step by step guidance

1. Step 1: Identify the given slope and point. The slope is \(\frac{1}{3}\) and the line passes through the point \((4, 3)\).
2. Step 2: 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 given point. Substitute \(m = \frac{1}{3}\), \(x_1 = 4\), and \(y_1 = 3\) to get \(y - 3 = \frac{1}{3}(x - 4)\).
3. Step 3: To graph the line, start by plotting the point \((4, 3)\) on the coordinate plane.
4. Step 4: Use the slope \(\frac{1}{3}\), which means rise over run is 1 up and 3 to the right. From the point \((4, 3)\), move up 1 unit and right 3 units to find a second point on the line.
5. Step 5: Draw a straight line through the two points. This line represents the graph of the equation with slope \(\frac{1}{3}\) passing through \((4, 3)\).