Graphing equations, slopes, and y-intercepts

How do you write an ordered pair? (3 steps)

1. Begin with the x-value, which you'll find by counting how far to the right of left the point is from the y-axis. 2. Then find the y-value by counting how far, up or down, the point is from the x-axis. 3. Put these two numbers in your paratheses. It will always be (x, y)

How do you find the solution to 2 equations by graphing? (4 steps)

1. Find the b and m for each equation. 2. Graph both lines. (Doing this in different colors can help.) 3. Find the point where the two lines meet. 4. Write the solution in an ordered pair.

On a graph, how do you find "m"? (5 steps)

1. Pick two points. Label them as "point 1" and "point 2" or make them different colors. 2. Focus on the rise (up or down) from one point to the other. 3. Find the run (left or right) from the same point as in part 2 to the other. 4. Put rise over run in a fraction 5. Simply, if possible

Which directions create a negative value?

Down, left

What is your goal and what are the steps you take when a line's equation is not in y=mx+b form? (example: 3x+4y=16) (4 steps)

Goal: Isolate y on the left side of the equal sign Step 1: Subtract mx or b if they are on the same side as y. (In this example, subtract 3x from both sides. You now have 4y=16-3x) Step 2: If there is a number attached to y, divide both sides by that number. (In this example, we would divide both sides by 4 to get y=16/4-3/4x) Step 3: On the right side of the equal sign, if b and mx are not in the correct order, switch them. (In this example, you would turn y=16/4-3/4x to y=-3/4x+16/4) *Note: be very careful of negative/minus signs. Make sure you keep them consistent Step 4: Simply when possible (In our example, you can simply the 16/4 to 4, making your equation y=-3/4+4)

When you're writing your own equations, which letters in y=mx+b are you looking to replace with numbers?

JUST m and b

How do you find "b"?

Look for the place where the line crosses the y-axis and count where that is on the y-axis. (Your x-value will always be 0.)

If rise OR run is negative, is the slope negative or positive?

Negative

If rise AND run are negative, is the slope negative or positive?

Positive

What does "m" stand for?

Slope

What is the solution is two lines have the same slope (m) and the same y-intercept (b)?

These equations will create the same line. The solutions are infinite.

What is the solution if two lines have the same slope (m) but different y-intercepts (b)?

These lines are parallel. They will never cross/intersect and have no solution.

What does it mean if an equation only has a y-value? (ex. y=7)

This is a horizontal line. In this example, y will be 7, no matter what x is.

What does it mean if an equation only has an x-value? (ex. x=-3)

This is a vertical line. In this example, x will be -3, no matter what y is.

What does it mean if an equation doesn't show a "b" value? (y=2x)

This means that b=0

What does it mean if an equation doesn't show an "m" value? (ex. y=x+6)

This means that m=1

Which directions create a positive value?

Up, right

When do you count the distance from one point to another?

When calculating the line's slope

When do you count one point's distance from the x and y axes?

When writing an ordered pair

What is the equation we use when we are graphing a line?

Y=mx+b

What does "b" stand for?

y-intercept