1-Use the point-slope form of the equation to identify a point the line passes through and the slope of the line. y-1=5(x-3)

1. Break Down the Problem

To utilize the point-slope form of a linear equation, we need to identify both a specific point on the line and the slope of the line represented by the equation in point-slope form.

2. Relevant Concepts

The point-slope form of a line is given by the equation: $y - y_1 = m(x - x_1)$ where $(x_1, y_1)$ is a point on the line and $m$ is the slope.

In the given equation $y - 1 = 5(x - 3)$:

• The slope $m$ can be directly identified as 5.
• The point $(x_1, y_1)$ can be determined from the term $y - 1$ and $x - 3$.

3. Analysis and Detail

By analyzing the equation $y - 1 = 5(x - 3)$:

• Comparing with the point-slope form:
  • $y_1 = 1$
  • $x_1 = 3$
• Therefore, the point the line passes through is $(3, 1)$ and the slope of the line is $5$.

4. Verify and Summarize

The equation is correctly structured as a point-slope form. Hence, we have confirmed:

• Point on the line: $(3, 1)$
• Slope of the line: $5$

Final Answer

The point the line passes through is $(3, 1)$ and the slope of the line is $5$.