# Linear Equations

### y=mx

## The following VOCABULARY should be put into your spiral.

**PROPORTIONAL RELATIONSHIP:**Two quantities x and y have a proportional relationship if y is always a constant multiple of x. A relationship is proportional if it can be described by equivalent ratios.

**EQUATION: **An equation is a mathematical sentence that includes an equals sign to compare two expressions. Example: y=mx, such as 8=4(2)

**LINEAR EQUATION: **An equation is a linear equation if the graph of all its solutions is a line. **Example: **y=1/4x + 5 is a linear equation because the graph of its solutions is a line.

**ORIGIN: **The origin is the point of intersection of the x-axis and y-axis on a coordinate plane (0,0).

## Draw this graph in your spiral. Now label the y-axis, x-axis, origin and all four quadrants. | ## Plotting Points - Plot the 4 points below on the graph you just labeled in your notes.Remember when plotting points you always start at the origin. Next you go left (if x-coordinate is negative) or right (if x-coordinate is positive. Then you go up (if y-coordinate is positive) or down (if y-coordinate is negative) Plot these 4 points
A (3, -4), B (5, 6), C (-4, 5) and D (-7, -5) | ## y = mx (write the notes on y=mx in your spiral)In the equation y=mx, m will always represent the constant multiplier. This is the number that you will multiply x by. We say it is constant because it will not change. Every time you use a different x value, the y value will change because of the constant multiplier, m. y=mx will |

## Plotting Points - Plot the 4 points below on the graph you just labeled in your notes.

Remember when plotting points you always start at the origin. Next you go left (if x-coordinate is negative) or right (if x-coordinate is positive. Then you go up (if y-coordinate is positive) or down (if y-coordinate is negative)

Plot these 4 points

A (3, -4), B (5, 6), C (-4, 5) and D (-7, -5)

## y = mx (write the notes on y=mx in your spiral)

In the equation y=mx, m will always represent the constant multiplier. This is the number that you will multiply x by. We say it is constant because it will not change. Every time you use a different x value, the y value will change because of the constant multiplier, m.

y=mx will **always** pass through the origin. Write in your journal why this is true.

## Slope - Copy the graph to the right into your spiral and write what is in bold into your spiral.

Slope is the ratio of the vertical rise to the horizontal run between any two points on a line. Usually referred to as the rise over run. It also represent the letter m in the equation y=mx.

The slope in this case is 10/6 because starting at the line where it crosses the x-axis you counted up 10 units (the rise) and then you counted over 6 units to get back to the line (the run). You always put the rise as the numerator and the run as the denominator.