Geometry A 2.3 Equations of Lines

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear equation?

Back

The slope (m) represents the rate of change of y with respect to x, indicating how steep the line is.

Front

What does the y-intercept (b) represent in a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis, indicating the value of y when x = 0.

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the equation of a line with a slope of 0?

Back

The equation of a line with a slope of 0 is a horizontal line, represented as y = b, where b is the y-coordinate of any point on the line.

Front

What is the equation of a line with an undefined slope?

Back

The equation of a line with an undefined slope is a vertical line, represented as x = a, where a is the x-coordinate of any point on the line.

Front

If a line has a slope of 2 and passes through the point (1, 3), what is its equation?

Back

Using the point-slope form, the equation is y - 3 = 2(x - 1), which simplifies to y = 2x + 1.

Front

What is the x-intercept of a line?

Back

The x-intercept is the point where the line crosses the x-axis, which occurs when y = 0.

Front

How do you convert the standard form of a linear equation Ax + By = C to slope-intercept form?

Back

To convert, solve for y: y = (-A/B)x + (C/B). The slope is -A/B and the y-intercept is C/B.

Front

What is the relationship between parallel lines in terms of slope?

Back

Parallel lines have the same slope but different y-intercepts.