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point slope form

where m is the slope and (x1, y1) is a point on the line

y - intercept

the y-coordinate of the point where the line crosses the y-axis

1 - Write ƒ(0) = 5 as (0, 5) and ƒ(4) = 17 as (4, 17)

Ex: Write an equation for the linear function ƒ with the values ƒ(0) = 5 and ƒ(4) = 17.

How to Write an Equation of a Line in Slope-Intercept Form

1 - Identify the slope m. You can use the slope formula if you know two points on the line.

standard form

can be used to find the x- and y-intercepts.

the slope and the y-intercept

What do you need to graph a line?

plug the slope and a point into y = mx + b

Write the equation of a line that passes through the point with the given slope

use the formula to find the slope

Write the equation of a line in slope intercept form that passes through two points

Converse

(noun) A statement that switches the hypothesis and conclusion

parallel lines

2 lines that never cross/intersect and stay the same distance apart

1 - Identify the slope (in this case = 3)

Write an equation of the line that passes through (-3, -5) and is parallel to the line y = 3x - 1

Perpendicular lines

lines in a plane that intersect to form 4 right angles

To determine whether lines are parallel or perpendicular

write all equations in slope-intercept form ( y = mx + b)

Scatter plot

is a graph used to determine whether there is a relationship between paired data. Scatter plots can show trends in data.

positive correlation

y tends to increase, as x increases

negative correlation

y tends to decrease, as x increases

Relatively No Correlation

x and y have no apparent relationship

line of best fit

The line that most closely follows a trend in data is called the best-fitting line.

Linear Regression

the process of finding the best-fitting line to model a set of data; you can use technology to do this

Linear Interpolation

using a line or its equation to approximate a value between two known values

Interpolate Using an Equation

1 - Make a scatter plot of the data

Linear Extrapolation

using a line or its equation to approximate a value outside the range of known values

Zeros of a Function

for the function ƒ, any number x such that ƒ(x) = 0