How to find the coordinates of a point on a straight line?

To find the coordinates of a point on a straight line, you will need to know the equation of the line and the position of the point relative to the line.

1. Start by writing down the equation of the straight line in the form y = mx + b, where m is the slope of the line and b is the y-intercept. If the equation is given in a different form, such as Ax + By = C, you can rearrange it to the slope-intercept form.

2. Determine the position of the point on the line. If the point is given as (x, y), substitute the x-value into the equation of the line to find the corresponding y-value. If the point is given as (x, mx + b), you can directly use these values.

3. Once you have the x and y values of the point, the coordinates of the point on the line are (x, y).

Method 1: Using Point-Slope Form

Step 1: Determine the slope of the line.

Step 2: Choose a known point on the line, denoted as (x₁, y₁).

Step 3: Use the point-slope form: y - y₁ = m(x - x₁)

where m is the slope and (x₁, y₁) is the known point.

Step 4: Substitute the slope and known point into the equation.

Step 5: Solve for y or x by isolating the variable.

Method 2: Using Two-Point Form

Step 1: Choose two known points on the line, denoted as (x₁, y₁) and (x₂, y₂).

Step 2: Use the two-point form: (y - y₁) / (x - x₁) = (y₂ - y₁) / (x₂ - x₁)

Step 3: Substitute the coordinates of the two points into the equation.

Step 4: Simplify the equation to find the slope, m = (y₂ - y₁) / (x₂ - x₁).

Step 5: Choose one of the known points and use the point-slope form as in Method 1 to find the coordinates of the new point.

Note: If the line is vertical (parallel to the y-axis), use the equation x = x₁ for any value of y.