Step-by-step explanation:
First, find the slope using the slope formula
m = (Y2 - Y1)/(X2 - X1).
Then use the point slope formula,
Y - Y1 = m(X - X1), with one of the given
points and the slope. Also, solve for y.
Use Y - Y1 = m(X - X1)
Also, solve for y.
Find the slope of the given line, m, by rewriting the given equation in y = mx + b. Flip and change the sign on the given slope to find the new slope.
Use Y - Y1 = m(X - X1)
Plug in the given point and new slope
and solve for y.
Plot points or graph line. Move a vertical line across the graph. If the line touches more than once then it is not a function.
Domain = { x-values, ... }
Range = { y-values, ... }
List the elements in increasing order and don't repeat.
For this class, the domain is all real numbers unless you have an x in the denominator of a fraction.
When x is in the denominator, set the denominator equal to zero and solve. Everything on a number line works except the value(s) you got when solving.
Answer: (- infinity, #) u (#, infinity)
Parentheses everywhere b/c the number # does not work in the equation.
Domain: Squish the graph to the x-axis. Write shaded part in interval notation (left, right)
Range: Squish the graph to the y-axis. Write shaded part in interval notation (down, up)
Brackets include points, parentheses don't. Infinities always get parentheses.
Write both equations in the style y = mx + b.
Look at the slopes, m, to answer the question.
If the slopes are the same, then they are parallel.
If the slopes are negative reciprocals, then they are perpendicular. Otherwise, neither.
If you have an equal to under the inequality, then you have a solid boundary line. If you don't have an equal to under the inequality, then you have a dotted boundary line.
After you have graphed the boundary line and determined if it is solid or dotted, find a test point on either side of the boundary line. Substitute the ordered pair into the original inequality. If it simplifies down to a true statement, shade the region where that point is. If it is false, shade the region that does not contain that point.
so. you can pretty much skip that one, though is a valid critical point, the width can't clearly be 0