what we now call just the
"slope" was once called the "modulus of slope", the word
"modulus" being used in its sense of "number used to
measure" (as in "Young's modulus").
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Given a straight line with slope m and a point (p,q) on the line, the point-slope formula of the line is (y - q) = m(x - p) It is used to represent a straight line in the Cartesian plane. This allows techniques of algebra to be used in solving problems in geometry.
y-y1=m(x-x1) this is the answer
For a horizontal line, the slope is zero. Using the formula y=mx+b, where m is the slope.
The slope intercept formula is y=mx + b in which m is the coefficent by x, x is the slope, and b is the y-intercept which is why it is called y-intercpet or slope-intercept. An example: y=3x + 7. Here your slope is three and y-intercept 7.
slope can be represented by any variables, such that, the variable representing the slope is defined. by convention, mathematicians and mathematics books authors used and are using "m" as the variable for slope. (recommended to have further historical research on this matter)