Final answer:
The line represents the equation y = (2/3)x - (2/3) and passes through the point (4, 2) with a slope of 2/3.
Step-by-step explanation:
To draw a line through the point (4,2) with a slope of 2/3, we can use the point-slope form of a linear equation.
Here's how:
- 1. The point-slope form of a linear equation is given by y - y₁ = m(x - x₁), where (x₁, y₁) represents a point on the line, and m represents the slope of the line.
- 2. Substitute the given values into the equation: y - 2 = (2/3)(x - 4).
- 3. Simplify by distributing the slope: y - 2 = (2/3)x - (8/3).
- 4. Further simplify by adding 2 to both sides of the equation: y = (2/3)x - (8/3) + 2.
- 5. Combine like terms: y = (2/3)x - (8/3) + 6/3.
- 6. Simplify the right side of the equation: y = (2/3)x - (2/3).
- 7. Rearrange the equation to slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept: y = (2/3)x - (2/3).
- 8. Now, you can plot the line on a graph by selecting some x-values and finding the corresponding y-values using the equation. For example, if x = 0, y = (2/3)(0) - (2/3) = -2/3. Thus, one point on the line is (0, -2/3).
- 9. Similarly, if x = 3, y = (2/3)(3) - (2/3) = 2 - (2/3) = 4/3. Another point on the line is (3, 4/3).
- 10. Connect the plotted points with a straight line, extending it infinitely in both directions.