Algebra - 3.4 Use Slope to Write Linear Equations
What are the three ways of finding the slope of a linear equation?
1. graph it and count units to find rise over run. 2. find two points on the line and use slope formula. 3. rewrite the equation in slope intercept form.
What is point-slope form?
Using one known coordinate and the lines slope, you can find the lines equation (slope-intercept,) by solving the following point slop equation: y-y1=m(x-x)
What is a Linear Equation?
an equation with two variables and multiple solutions; its solution set forms a line when graphed on a coordinate plane.
Define Parallel Lines:
different lines that lie on the same plane and never intersect; Parallel lines have the same slope.
In algebra, what is the formula finding the slope of a line?
m is used to represent slope, so: m=y2-y1 over, or divided by y2-y1 When you use the formula, make sure that you decide which point will be (x2, y2) and which will be (x1, y1). It doesn't matter which point you choose, but you must be consistent.
How do you find the slope of a line when given two of its points?
m=y2-y1 over x2-x1
Define Reciprocal:
the inverse of a number; the product of a number and its reciprocal is 1.
What is slope intercept form?
y=mx+b, where m represents slope and b represents the y-intercept. Remember, the y-intercept is the point at which the graph of a line crosses the y-axes.
What three steps are taken to find the equation of a line that passes through 2 points?
1. Use the two points to find the slope. 2. Choose one of the points and use the point-slope form to write the equation. 3. Check to make sure the remaining point will make the equation true.
Since division by zero is undefined, a slope with a run of zero is what:
Undefined
Define Reciprocal:
A mathematical expression or function so related to another that their product is one; the quantity obtained by dividing the number by a given quantity.
A line that moves downward from left to right has which: a Positive or a Negative slope?
A negative slope.
A line that moves upward from left to right has which: a positive or a negative slop?
A positive slope.
What is Slope?
A ratio comparing rise to run.
define perpendicular:
At an angle of 90 degrees to a given line, plane, or surface.
How can you determine the slope when given two different coordinates?
By finding the change in x- and y-values, since this is the same as counting units on a coordinate plane.
Define Perpendicular Lines:
Lines that lie in the same plane and intersect at right angles; perpendicular lines have slopes that are negative reciprocals.
If you have a point on the line (x1,y1) and the slope which form should you use? slope-intercept or point-slope?
Point-slope
If you have the slope (m) and y-intercept (b) of a line, which form should you use to write its equation: slope-intercept or point-slope?
Slope-intercept
What are the 4 Steps used to determine slope?
Step 1: locate the two points. Step 2: Count units to find the distance the line travels up or down between the points Step 3: Count units to find the distance the line travels left or right. Step 4: Write a ratio comparing the vertical distance to the horizontal distance.
