Question

What does the equation "y=mx+c" mean?

Answer 1

Hi..

The equation that is written as

y = mx + c

represents a straight line graph. At any place on the horizontal (or "x") axis the line passes through a particular place on the other (vertical, or "y") axis, where the two axes are at right-angles to each other (are perpendicular, in an L shape). At a place further along the horizontal axis, the line passes through another place on the other axis so that the two points are joined together by a perfectly straight line.

Whatever two different values you choose on the horizontal (x) axis, when you look up the values on the vertical (y) axis, the pair of coordinates (the (x,y) pair) will always be joined by a straight line. Because of this, if you are given two sets of coordinates (two (x,y) pairs) that are on the line graph you can then you have all the information you need to draw the line on the page.

The "y" in the equation is then the value you read off on the vertical (or y) axis (how high the point is on the page), the "x" is the value you read off the horizontal (or x) axis (how far along the point is on the page). The letter "m" is a number that represents the slope of the line, which is the number of units you go up the page per unit along the page (where a unit might be millimetres for example) when you follow the straight line. The letter "c" is a number that represents the place on the vertical (or y) axis where the straight line crosses that axis, called the intercept. All straight lines drawn on a page that obey the equation y = mx + c have a slope and intercept. The slope and intercept are just numbers that define the shape of the line, but we say that x and y are variables because they vary depending on which place on the x and y axis you read off when pin-pointing a particular place on the line graph. The pairs of values (x,y), or coordinates that are on the line graph vary in a fixed relationship to other as you move along the line in either direction.

The equation y = mx + c represents a straight line graph on the xy plane with slope m and intercept c.