Straight Lines Flashcards
Creating, reading, and interpreting linear graphs
What is a “coordinate”?
It’s two (sometimes 3) numbers inside brackets that tell you where a point is.
(x, y) or (x, y, z)
The first value tells you how far left/right it is from the origin. The second value tells you how far up/down it is from the origin.
What does “y-coordinate” mean?
It’s the second value in a coordinate (x,y).
What does “x-coordinate” mean?
It’s the first value in a coordinate (x,y).
What does “linear” mean when graphing?
It makes a straight line.
What does “x-intercept” mean?
Where the line crosses the x-axis.
We know the coordinate is (x, 0).
What does y-intercept mean?
Where the line crosses the y-axis.
We know the coordinate is (0, y).
What does “gradient” or “slope” describe in normal English words?
It describes how steep or slanty a line is.
How do you calculate the gradient if you are given two points?
How can we use the gradient to see that two lines are parallel?
Parallel lines have the same gradient.
How can we use the gradient to see that two lines are perpendicular?
The gradients of perpendicular lines are the negative reciprocal. For example,
What is the equation of a flat horizontal line?
f(x) = ___________
y = __________
What is “gradient-intercept” form and why is it the most useful?
y=mx+c
This is the only format the calculator accepts in test mode.
In the equation y=mx+c, which letter represents the y-intercept?
(Be careful to notice the sign in front of c. This is also part of the y-intercept.)
In the equation y=mx+c, which letter represents the gradient?
(Be very careful not to include “x”. This is only the number BEFORE the x. There is no x in the gradient; it’s just a number.)
What are the two methods to graph the equation Ax+By=C?
- Use algebra to rearrange the formula into gradient-intercept form (y=mx+c).
- Find the intercepts and connect the dots.
How do you graph a line of the form y=mx+c?
- Mark the y-intercept (which is c from the equation) on the y-axis.
- Use the gradient (which is m from the equation) to count to the next point.
- Count up/down
- Count over to the right
How do you find the equation of a line by looking at the graph?
- Look at the graph to find the y-intercept.
- Find a second point that goes through a perfect coordinate.
- Find the slope by count how far up/down and how far right you go from the left point to the right point.
- Write y=mx+c, where m is the slope and c is the y-intercept.
How do you calculate the gradient if given a line in standard form?
Rearrange the equation into gradient-intercept form.
How do you find the equation of a line, given in the form
Find it in gradient intercept form and rearrnage.
What are the steps to find the equation of any line?
- Write down y = mx + c
- Figure out the gradient and write it into that equation
y = 3x + c - Plug in any point (1, 2) they gave you and solve for c.
2 = 3(1)+c
-1 = c - Write down your equation with the m and c that you found.
y = 3x - 1
How do you find the midpoint between two points A and B?
Using the midpoint formula in the formula booklet, separately calculate the x- coordinate and y- coordinate of the midpoint.
How do you find some letter coordinate from a point if you already know the line?
Plug the point into the line and solve.
How do you find the y-intercept of an equation in standard form?
Plug in 0 for x.
How do you find the x-intercept of an equation in standard form?
Plug in 0 for y.
How are straight lines related to right anges?
For example, “Determine, giving a reason, whether angle ACB is a right angle.”
Perpendicular lines make right angles.
You should show that the gradients of AC and CB are perpendicular (or not).
How do you find the equation of a line parallel to another line?
For example, y = 2x + 8?
- Find the gradient of the original line. This is also the gradient of the new line.
- Find a point that goes on the line (this is usually given).
- Plug the point (x,y) and gradient, m, into the equation y=mx+c and solve for c.
- Write y=mx+c, where m is the slope and c is the y-intercept.
How do you find the equation of a line perpendicular to another line?
For example,
- Identify the gradient of the original line. The gradient of the new line is the negative reciprocal of this.
- Find a point that goes on the line (this is usually given).
- Plug the point (x,y) and gradient, m, into the equation y=mx+c and solve for c.
- Write y=mx+c, where m is the slope and c is the y-intercept.
How do you find the equation of a line by looking at the graph?
- Look at the graph to find the y-intercept.
- Find a second point that goes through a perfect coordinate.
- Find the slope by count how far up/down and how far right you go from the left point to the right point.
- Write y=mx+c, where m is the slope and c is the y-intercept.
Plug the point (8,y) into your line equation and solve for y.
How do you rearrange a line equation into the form
- Multiply EVERYTHING by the biggest denominator.
- Move all terms to one side.
How do you find the distance bewteen 2 points?
For example, (0,4) and (8,0)
Either create a right-angled triangle on the graph and use the pythagorean theorem or use the distance formula in the booklet.
How do you find the midpoint of two coordinates?
You plug the points into the midpoint formula from the formula booklet. (Calculate each coordinate one at a time.)
How do you find a variable, given the midpoint of two coordinates?
For each coordinate separately, you plug the points into the midpoint formula and solve.
What part of a straight line are we talking about when we say “rate of change”?
gradient
The gradient represents rate of change. If you’re asked to “interpret” the gradient in a real-life situation, say that it represents the rate of change.
