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The coordinates of a point satisfy the equation of a line if the point is on the line

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This afirmation is true. A linear equation can be expressed in the form y=mx+b In this equation, x and y are coordinates of a point, m is the slope, and b is the y-coordinate of the y-intercept. Because this equation describes a line in terms of its slope and its y-intercept, this equation is called the slope-intercept form.
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