Math Blog Week 16

This week on math we learned about the equations of slopes.

There are 3 different equations for calculating the slope of a line: in the equation y=mx+b m represents the slope, y represents the y coordinate, x the x coordinate, and b the y-intercept.

The slope of a line is its \frac{rise}{run} so a whole number would be a fraction. The y-intercept is equal to y if x equals 0.

If the value of y equals 3, x equals 1 and the slope equals 4 we would have the equation 3=4\cdot1+b. On a graph it would look like this:  from this graph we can tell that since the y-intercept is -1, b=-1 so our equation to determine y on the graph is y=4x-1.

General form is much less useful, general form is represented by Ax+By+C where B and C are integers and A is a whole number. We can’t find the slope and equation from general form alone however if we convert it into the above form we can. If the equation is 3x-4y+8=0 first we add 4y to both sides of the equation so we get 3x+8=4y then we divide the equation by 4 which is the coefficient of the y \frac{3}{4}x+2=y

The final equation is slope-point form which is represented as y-y(1)=m(x-x(1)) if the slope equals \frac{3}{4} and the line goes through point (1, 4) then the equation will be y-4=\frac{3}{4}(x-1)

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