To write an equation in point-slope form, we need to have a point on the line and the slope of the line. Let's assume that we have the graph of a line represented as points (x₁, y₁) and (x₂, y₂).
1. First, we need to identify two points on the line from the graph. These points can be any two points that lie on the line.
2. We can then calculate the slope of the line using the formula:
slope = (change in y)/(change in x) = (y₂ - y₁)/(x₂ - x₁)
3. Once we have the slope, we can use any point on the line and the slope to write the equation in the point-slope form. Let's use the point (x₁, y₁) as our reference point.
4. The point-slope form of an equation is: y - y₁ = m(x - x₁), where (x₁, y₁) represents the coordinates of the point on the line, and m represents the slope.
5. Substitute the values of the slope and the coordinates (x₁, y₁) into the point-slope form equation. It will look like: y - y₁ = slope(x - x₁).
6. Simplify the equation by distributing the slope to both terms within the parentheses. The equation should then be written as:
y - y₁ = slope * x - slope * x₁
7. Finally, we can write the equation in point-slope form by moving the y₁ term to the other side of the equation. This will result in:
y = slope * x - slope * x₁ + y₁
8. If you are given specific points on the graph with coordinates (x₁, y₁), you can substitute them into the equation to get the final equation in point-slope form.
Remember, the point-slope form represents a linear equation and can be used to describe the graph of a line using the slope and a point on the line.
Explain how to write an equation in point-slope form for the graph provided. Use as much detail as you can in your explanation
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