Unit 6 Review Linear Functions

Slope on a One to One Grid

On a one-to-one grid, we can count slope using the boxes. Slope = \frac{\text{rise}}{\text{run}}

Review

The equation to calculate the y coordinate from the x coordinate on a line can be written in the form:

    \[y=mx+b\]

…where m is the slope (also known as gradient or rate of change), and b is the point on the line where the line cuts the y axis, that is, the y intercept.

When given two points, we can calculate slope using the formula

    \[m=\frac{y_2-y_1}{x_2-x_1}\]

Once we know the slope, we can calculate the value b by substituting one point in for the x and y; or we can use the formula

    \[y-y_1=m(x-x_1)\]

The intercepts are points on the axes. To calculate the y intercept, we substitute x=0 to the equation of the line. To calculate the x intercept, we substitute y=0 to the equation of the line.

Vertical lines have an equation such as x=5.

Horizontal lines have an equation such as y=7.

Parallel lines have the same slope. E.g. y=\frac{3}{4}x+5 and y=\frac{3}{4}x-12 are parallel.

Perpendicular lines are lines that intersect at 90°. If the first line has slope \frac{a}{b} then the second line will have slope \frac{-b}{a}: the negative reciprocal. Eg, the lines y=\frac{3}{4}x+5 and y=-\frac{4}{3}x-12 are perpendicular. As another example, the lines y=\frac{1}{2}x+5 and y=-2x+5 are perpendicular.

Practice

Use this applet to practice calculating the slope between two points; finding the equation of a line; calculating the y-intercept and calculating the x-intercept.