Q1. Find an equation of the line with slope that passes through the point . Write the equation in the form .

Background

Topic: Linear Equations (Point-Slope and Standard Form)

This question tests your ability to write the equation of a line when given a slope and a point, and then convert it to standard form ().

Key Terms and Formulas

• Slope (): The steepness of the line, given as .

• Point-Slope Form: , where is a point on the line.

• Standard Form: , where , , and are integers, and should be positive.

Step-by-Step Guidance

1. Start by writing the point-slope form of the equation using the given point and slope :

2. Simplify to :

3. Distribute the slope to both terms inside the parentheses:

4. Calculate and write the equation with all terms shown:

5. To write the equation in standard form , move all terms involving and to one side and constants to the other. Multiply both sides by 2 to clear fractions if needed.

Try solving on your own before revealing the answer!