Geometry A 2.3 Equations of Lines

Front

What is the slope-intercept form of a line?

Back

The slope-intercept form of a line 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; it indicates 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 equation of a line given the slope and a point?

Back

Use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

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-value.

Front

What is the equation of a vertical line?

Back

The equation of a vertical line is of the form x = a, where a is the x-value at which the line is located.

Front

If a line has a slope of -2, what does this indicate about its direction?

Back

A slope of -2 indicates that the line descends from left to right, meaning as x increases, y decreases.

Front

How do you convert from slope-intercept form to standard form?

Back

To convert to standard form (Ax + By = C), rearrange the slope-intercept equation to isolate x and y on one side.

Front

What is the significance of the slope being positive?

Back

A positive slope indicates that the line rises from left to right, meaning as x increases, y also increases.

Front

What is the significance of the slope being negative?

Back

A negative slope indicates that the line falls from left to right, meaning as x increases, y decreases.