This week, one of the most important things that I learned in Math 10 was equations of lines. I chose this as the subject for this week’s blog post because both being able to graph a line from an equation and being able to represent a line on a graph through an equation are important skills. Being able to know what kind of line an equation forms and how the different parts of an equation relate to a line allows you to know more about the equation, like what kind of slope it has and where the intercepts are. An equation of a line is what tells you where the line is on the graph, and the different parts of the equation determine different parts of forming the line. The equation and the line that it forms are equivalent to one another and an equation can be used to describe a line, which makes it important to know what it means and what line it would form by looking at it.

Parts of an equation of a line:

In an equation of a line, the number being multiplied by x is the slope of the line, and the other number in the equation is the y intercept. The equation shows that y is equal to x multiplied by the slope, combined with the y intercept.

Steps for forming a line from an equation or finding an equation from a line:

Step 1: The first step is to find the y intercept. If the equation of the line is given, finding the y intercept first allows you to plot a point from which you can use the slope to plot more points to form a line. To find the y intercept from an equation, you look at the number in the equation that is not multiplied by x; you then plot that point on the y axis to have your y intercept on the line. If you are given a line and need to convert it to an equation, you look at the y intercept (which is where the line crosses the y axis), and you take that number and add it to your equation, in the spot that is not being multiplied by x.

Step 2: The next step is to find the slope of the line. The slope of the line is the steepness of a line and is found using rise over run, which means finding the amount of points on the y axis that are between two points that the line has, and putting that number over the number that resulted from doing the same on the x axis. If you are given the equation and need to form the line, you take the slope, which is the number being multiplied by x, and you look at in in fraction form, considering that the numerator is the rise and the denominator is the run. You then start at the y intercept or another point on the line that you know, and move down or up depending on if the numerator is positive or negative, the amount of times as what the number is, and then do the same going across with the x axis for the run. If you are starting with a line and have to find the equation, you count how many points there are between the points of the line for both rise and run, put rise over run, and take that number as the slope to multiply by x in the equation.

Examples of equations of lines:

Positive line (red) :

y = 2x – 3

Step 1: Y intercept is -3 because it is the number in the equation not being multiplied by x, on the line we can see that the y intercept is -3 because that is where the line crosses through the y axis.

Step 2: The slope is 2 because that is the number in the equation multiplied by x. 2 is actually so the rise is 2 and the run is 1 which as you can see by looking at the graph is the amount of points on the x and y axis between each point on the line.

Negative line (blue) :

y = -5x +2

Step 1: Y intercept is 2 because it is the number in the equation not being multiplied by x, and it is the point on the line where the line crosses through the y axis.

Step 2: The slope is -5 because it is the number in the equation multiplied by x. -5 is actually so the rise is -5 and the run is 1; because the rise is negative it is going downwards instead of up, causing the line to be negative.