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

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

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

Step 1: Identify the coordinates of point C, which are (5, 5). This means x = 5 and y = 5.
Step 2: Identify the slope of the line, which is given as 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 a point on the line and m is the slope.
Step 4: Substitute the values into the point-slope form. Here, (x1, y1) = (5, 5) and m = 1. So, it becomes: y - 5 = 1(x - 5).
Step 5: Simplify the equation. Distribute the 1 on the right side: 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 the line is y = x.

Point-Slope Form – The point-slope form of a line is used to find the equation of a line given a point and a slope, expressed as y - y1 = m(x - x1).
Slope-Intercept Form – The slope-intercept form of a line is expressed as y = mx + b, where m is the slope and b is the y-intercept.