20 Questions
What is a key characteristic of a linear equation?
Plotting as a straight line on a graph
In which form does a linear equation have parts including the slope and y-intercept?
Slope-intercept form
What does the y-intercept represent in a linear equation?
The place where the line crosses the y-axis
If a linear equation has a slope of 0, what type of line does it represent on a graph?
A horizontal line
How can a linear equation be written using the slope and intercept values?
Determining the slope and y-intercept
What is the formula for a linear equation in the form y = mx + c?
y = 2x + 3
When creating a linear equation from two points (1,1) and (3,2), what is the slope (m) calculated to be?
0.5
For the linear equation y = 2x + c, if the point (1,1) is substituted, what is the value of c?
-1
Which formula can be used to calculate the slope of perpendicular lines?
$m1 \times m2 = -1$
In linear equations written as functions, what is another way to represent y = mx + c?
$f(x) = mx + c$
What is the standard form of a linear equation?
$ax + by = c$
If a linear equation has a slope (m) of 4 and crosses the y-axis at y = -3, what is the linear equation in slope-intercept form?
$y = 4x - 3$
What is the x-intercept of the linear equation 3x - 2y = 6?
(2, 0)
Which part of the linear equation $y = -5x + 2$ represents the slope?
-5
Given a linear equation in point-slope form as $y - 3 = 2(x - 1)$, what is the y-value of the point it passes through?
-3
What is the formula for calculating the slope (m) of a linear equation given two points (x1, y1) and (x2, y2)?
$m = \dfrac{y2 - y1}{x2 - x1}$
In the equation y = 2x + 3, what does the value of 3 represent?
Y-intercept (c)
What is the equation for finding the y-intercept (c) in a linear equation given two points (x1, y1) and (x2, y2)?
$c = x1 + \left(\dfrac{x2 - x1}{y2 - y1}\right)y1$
When creating a linear equation from two points, why is it important to be consistent with labeling them as (x1, y1) and (x2, y2)?
To avoid confusion and errors in calculations
In the context of making linear equations more identifiable, what is the purpose of writing linear equations as functions such as f(x), g(x), h(x), etc.?
To help with identification when dealing with multiple lines
Explore the definition and features of linear equations, including variables with exponents of one, straight line graphs, and the standard form of a linear equation. Learn about constants, y-intercepts, slopes, and x-intercepts.
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