You measure the gradient, which is rise/run or (change in vertical direction)/(change in horizontal direction). This is denoted by m. You also measure the height of the y-intercept: this is c.Then the equation is y = mx + c.
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An equation of a line requires two parameters. The slope, by itself, is not enough.
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Subtract the equation of one line from the equation of the other
By substitution
Substitute the coordinates of the point into the equation of the line. If the result is true, then the point is on the line.