Find the equation of the line that passes through the point (2, 3) and has a slo

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Question: Find the equation of the line that passes through the point (2, 3) and has a slope of -1.

Options:

Correct Answer: y = -x + 5

Solution:

Using point-slope form: y - 3 = -1(x - 2) => y = -x + 5.

Find the equation of the line that passes through the point (2, 3) and has a slope of -1.

Find the equation of the line that passes through the point (2, 3) and has a slope of -1.

Step 1: Identify the point through which the line passes. The point is (2, 3).
Step 2: Identify the slope of the line. The slope is -1.
Step 3: Use the point-slope form of the equation of a line, which is: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.
Step 4: Substitute the values into the point-slope form. Here, (x1, y1) = (2, 3) and m = -1. So, it becomes: y - 3 = -1(x - 2).
Step 5: Simplify the equation. Distribute -1: y - 3 = -x + 2.
Step 6: Add 3 to both sides to solve for y: y = -x + 2 + 3.
Step 7: Combine like terms: y = -x + 5.
Step 8: The final equation of the line is y = -x + 5.

Point-Slope Form – The equation of a line can be expressed using the point-slope form, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Slope-Intercept Form – The slope-intercept form of a line is given by y = mx + b, where m is the slope and b is the y-intercept.