If the coordinates of point C are (5, 5) and the slope of line AC is 1, what is

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Question: If the coordinates of point C are (5, 5) and the slope of line AC is 1, what is the equation of line AC? (2021)

Options:

Correct Answer: y = x

Exam Year: 2021

Solution:

Using point-slope form: y - 5 = 1(x - 5) => y = x

If the coordinates of point C are (5, 5) and the slope of line AC is 1, what is the equation of line AC? (2021)

If the coordinates of point C are (5, 5) and the slope of line AC is 1, what is the equation of line AC? (2021)

Step 1: Identify the coordinates of point C, which are (5, 5).
Step 2: Note the slope of line AC, which is given as 1.
Step 3: Use the point-slope form of a line equation, which is: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Step 4: Substitute the coordinates of point C (5, 5) into the equation: y - 5 = 1(x - 5).
Step 5: Simplify the equation: y - 5 = 1 * (x - 5) becomes y - 5 = x - 5.
Step 6: Add 5 to both sides to isolate y: y = x - 5 + 5, which simplifies to y = x.
Step 7: The final equation of line AC is y = x.

Point-Slope Form – The point-slope form of a line is used to write the equation of a line given a point on the line and its slope.
Slope – The slope of a line indicates its steepness and direction, calculated as the change in y over the change in x.
Linear Equations – Linear equations represent straight lines and can be expressed in various forms, including slope-intercept and point-slope forms.