Question

Складіть рівняння прямої, що проходить через точку А(-2;1) і утворює з додатним напрямом осі абсцис 45°.

Answer 1

Equation of a Line Passing Through Point A(-2,1) and Forming a 45° Angle with the Positive x-axis

To find the equation of a line that passes through point A(-2,1) and forms a 45° angle with the positive x-axis, we can use the slope-intercept form of a linear equation, which is given by:

y = mx + b

where: - m is the slope of the line, and - b is the y-intercept of the line.

To determine the slope of the line, we can use the fact that the line forms a 45° angle with the positive x-axis. The slope of a line is given by the tangent of the angle it forms with the x-axis.

Since the line forms a 45° angle with the positive x-axis, the tangent of this angle is 1. Therefore, the slope of the line is 1.

Now that we have the slope, we can substitute the coordinates of point A(-2,1) into the equation to find the y-intercept.

Let's substitute the values into the equation:

1 = 1*(-2) + b

Simplifying the equation:

1 = -2 + b

Adding 2 to both sides of the equation:

1 + 2 = b

b = 3

Therefore, the equation of the line that passes through point A(-2,1) and forms a 45° angle with the positive x-axis is:

y = x + 3.

Please let me know if there's anything else I can help you with!