I need it step by step please

The equation of the line passes through (3, -2) and parallel to the given line:

The equation of the line passes through (3, -2) and perpendicular to the given line:

Step-by-step explanation:

Given the points on the graph line

(2, -1)

(1, -4)

Finding the slope between (2, -1) and (1, -4)

Equation of the line passes through (3, -2) and parallel to the given line.

We know that parallel lines have the same slope.

so the equation of the line parallel to the given line = 3

Thus, using the point-slope form of the line equation

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = 3 and the point (3, -2)

Therefore, the equation of the line passes through (3, -2) and parallel to the given line:

The equation of the line passes through (3, -2) and perpendicular to the given line

We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:

slope = m = 3

perpendicular slope = – 1/m = -1/3 = -1/3

Therefore, substituting the values of perpendicular slope = -1/3 and the point (3, -2) in the point-slope form of the line equation

subtract 2 from both sides

Therefore, the equation of the line passes through (3, -2) and perpendicular to the given line:

Conclusion:

The equation of the line passes through (3, -2) and parallel to the given line:

The equation of the line passes through (3, -2) and perpendicular to the given line:

answer: options?

step-by-step explanation:

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step-by-step explanation:

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