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Identify the equation of the line that passes through two given points, illustrating the application of the point-slope formula.

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Final answer:

To identify the equation of a line, calculate the slope with the formula (Y₂ - Y₁) / (X₂ - X₁) using given points, then apply the point-slope formula, and finally convert to slope-intercept form (y = mx + b).

Step-by-step explanation:

To identify the equation of a line that passes through two points, we first need to calculate the slope of the line (m) using the formula m = (Y₂ - Y₁) / (X₂ - X₁), where (X₁, Y₁) and (X₂, Y₂) are the given points. Once we have the slope, we can use the point-slope formula, y - Y₁ = m(x - X₁), to write the equation of the line. If we want the equation in slope-intercept form (y = mx + b), we solve the point-slope equation for y and determine the y-intercept (b), which is the point where the line crosses the y-axis. An example is provided by Figure A1, where the line has a slope of 3 (rise over run), and the y-intercept is 9. With this information, the equation can be written as y = 3x + 9.

By applying these steps to specific points, we can find the exact equation of the line that fits our data.

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