What are the three forms of linear equations?

Slope-intercept, standard, point-slope forms.

How is slope defined in linear equations?

Represents rise over run, trend direction.

X-intercepts at y = 0, y-intercepts at x = 0.

Parallel lines have equal slopes.

Perpendicular lines have negative reciprocal slopes.

The slope of a line indicates its steepness, with positive slopes going up, negative slopes going down, and a slope of 0 for horizontal lines.
Understanding the different forms of linear equations (slope-intercept, standard, point-slope) is crucial for graphing lines accurately, with each form providing unique insights into the equation's behavior.

What are the three forms of linear equations?
Slope-intercept, standard, point-slope forms.
How is slope defined in linear equations?
Represents rise over run, trend direction.
How are x-intercepts and y-intercepts defined in linear equations?
X-intercepts at y = 0, y-intercepts at x = 0.
What is the relationship between slopes of parallel lines?
Parallel lines have equal slopes.
How are perpendicular lines defined in terms of slopes?
Perpendicular lines have negative reciprocal slopes.

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Linear equations can be written in three forms: slope-intercept form (y = mx + b), standard form (ax + by = c), and point-slope form (y - y1 = m(x - x1).
The slope in a linear equation represents the rise over the run, with positive slopes indicating an upward trend and negative slopes indicating a downward trend.
The slope of a line at a 45-degree angle is 1, while steeper angles have higher slope values.
Horizontal lines have a slope of 0, while vertical lines have an undefined slope that can reach infinity.
The slope between two points (x1, y1) and (x2, y2) is calculated as (y2 - y1) / (x2 - x1).
X-intercepts occur where y = 0, while y-intercepts occur where x = 0 in a linear equation.
Parallel lines have the same slope, denoted by m1 = m2, while perpendicular lines have slopes that are negative reciprocals of each other, m1 = -1/m2.
Graphing linear equations involves identifying the slope and y-intercept to plot points and connect them with a straight line.
In slope-intercept form (y = mx + b), the slope (m) and y-intercept (b) are crucial for graphing the equation.
Standard form equations (ax + by = c) can be graphed by finding the x and y-intercepts, replacing y with 0 to find x-intercept and x with 0 to find y-intercept.

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To graph the linear equation 4x + 3y = 12 in standard form, first find the x-intercept by setting y to zero, resulting in x = 3. Then, find the y-intercept by setting x to zero, yielding y = 4. Connect these points with a straight line to graph the equation.
For an equation in point-slope form like y - 3 = 2(x - 2), identify the slope (2) and the point (2, 3) through which the line passes. Plot this point and use the slope to find additional points, like 3, 5, and -3, -1, to draw the line.
When graphing an equation like y + 4 = -3/2(x + 1), determine the slope (-3/2) and the point (-1, -4). Plot this point and use the slope to find another point, like -3, -1, to sketch the line.
To graph y = 3, draw a horizontal line at y = 3, creating a constant line. For x = 4, draw a vertical line at x = 4. Horizontal lines have a slope of 0, while vertical lines have an undefined slope.