Slope of a Line

Slope Slope describes the slant or direction of a line.

Given two points (x 1, y 1 ) and (x 2, y 2 ), the formula for the slope on the straight line going through these two points is:

Slope The subscripts indicate that you have a "first" point and a "second" point. Slope is sometimes referred to as "rise over run", the fraction consists of the "rise" (change in y, going up or down) divided by the "run" (change in x, going to the left or right).

The two points shown are: (0, -4) and (-3, -6). Now we have two points we can put them in the slope formula:

Example #2

Find the slope: (-3, 6) and (5, 2)

Horizontal Lines The points (-3, 4) and (5, 4), the slope is: For every horizontal line: a slope of zero means the line is horizontal, and a horizontal line means you'll get a slope of zero. The equation of all horizontals lines are of the form: y = “a number“ (ex. y = 4)

Vertical Lines Now consider the vertical line of the equation x = 4 : A vertical line will have no slope, and “the slope is undefined" means that the line is vertical. The equation of all vertical lines are of the form x = “a number“ (ex. x = 4).

1. Positive Slope 2. Negative Slope 3. Zero Slope 4. Undefined Slope A line that rises from left to right A line falls from left to right A line is horizontal The line is vertical

Find the slope of a line that contains points: (5, 4) and (5, 2). This slope is undefined.

Find the Slope (5, -2) (11, 2) (3, 9) Red Blue Green

Am I going Too fast? Let’s do it Slower!

Q & A If I am given a line, how do I find the slope? Pick any two points on the line and use the slope formula.

Q & A If I pick two different points then some else won’t I get a different answer? No, the math will be different, but the answer will be the same.

First pick any two points on the line. Then find the coordinates of the points and use them in the slope formula. (5,6) (-4,-2)

Q & A What is the slope formula?

Intercepts and Point-Slope Form

The x-intercept of a straight line is the x-coordinate of the point where the graph crosses the x-axis. The y-intercept of a straight line is the y-coordinate of the point where the graph crosses the y-axis. Definition - Intercepts x-intercept y-intercept BACK

Intercepts x y 0 0 ? ? Finding the x-intercept & y-intercept is like filling in this t-table when x = 0 and you solve for y, and when y = 0 solving for x. BACK

Finding the intercepts 3x + y = 6 To find the x-intercept, let y = 0 3x + (0) = 6 3x = 6 BACK

Finding the intercepts 3x + y = 6 To find the y-intercept, let x = 0 3(0) + y = 6 y = 6 BACK

The graph of 3x + y = 6 x-intercept = 2 y-intercept = 6 BACK

Find the intercepts and graph 3x + 4y = 12 BACK

Finding the x-intercept 3x + 4y = 12 3x + 4(0) = 12 3x + 0 = 12 3x = 12 x = 4 BACK

Finding the y-intercept 3x + 4y = 12 3(0) + 4y = y = 12 4y = 12 y = 3 BACK

The graph of 3x + 4y = 12 x-intercept = 4 y-intercept = 3 BACK

Find the intercepts and graph y = 4x - 4 You try this one. BACK

Finding the x-intercept y = 4x = 4x = 4x = 4x 1 = x BACK

Finding the y-intercept y = 4x - 4 y = 4(0) - 4 y = -4 BACK

The graph of y = 4x - 4 x-intercept = 1 y-intercept = -4 BACK

The x-intercept occurs when y = 0 ( 2, 0) The y-intercept occurs when x = 0 (0, -3) Name the x-intercept and the y-intercept of the equation graphed below. BACK

Point Slope Form/Equation Builder BACK

Point Slope Form Draw your first point at (-2,1) and use the slope of 3 to add addition points to your line. BACK

Slope Intercept Form & Graphing

y = mx + b Slope-Intercept Form BACK y = 5x + 2

Up 1, Right 3. Up 2, Left 1. Down 2 Right 3 or Up 2, Left 3 BACK

Finding the slope and y-intercept State the slope and y-intercept of: y = 3x + 2 BACK

Up/Down Left/Right The slope is 3 or 3/1 which means up 3 and right 1. BACK

y = 3x + 2 Slope = 3/1 y-intercept= 2 Up 3 and Right 1 BACK

y = -2x + 3 Slope = -2/1 y-intercept= 3 Down 2 and Right 1 BACK

y = 3x -2 You try this one BACK

y = 3x -2 BACK

Changing equations to the form y = mx + b When equations are in different forms, then you need to change them to y = mx + b BACK

Changing equations to the form y = mx + b BACK

2x + 4y = 8 changed to y = -1/2x + 2 y-intercept= 2 Slope = -1/2 Down 1 Right 2 BACK

Now you change 2x + 3y = 6 to y = mx + b BACK

2x + 3y = 6 changed to y = -2/3x + 2 BACK

Parallel Lines Same or different The equations of two parallel lines have the same slope, but two different y-intercepts.

y = 3x + 4 and y = 3x - 2 y = 3x + 4 y = 3x -2 BACK

What if there is no constant? If you have a problem like: y = 3x You can add a zero, “+ 0”, to the equation without changing the value. BACK

Hints If y = x + 3,the coefficient of x is 1, so the slope is 1/1. If you do not have room to graph a slope of 2/1 you can use the equivalent fraction -2/-1 BACK

Sloping lines with different gradients. Gradient is the mathematical word for steepness. The bigger the gradient, the steeper the slope of the line. A line that slopes up has a positive gradient A line that slopes down has a negative gradient.