Writing An Equation From A Graph

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented as 'm' in the equation of a line (y = mx + b). It is calculated as the change in y divided by the change in x (rise/run).

Front

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

Back

The y-intercept is the point where the line crosses the y-axis. In the equation y = mx + b, 'b' represents the y-intercept.

Front

How do you find the equation of a line given two points?

Back

To find the equation of a line given two points (x1, y1) and (x2, y2), first calculate the slope (m = (y2 - y1) / (x2 - x1)). Then use the point-slope form: y - y1 = m(x - x1).

Front

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

Back

The point-slope form of a linear equation is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How can you determine if a line is increasing or decreasing?

Back

A line is increasing if the slope (m) is positive, and it is decreasing if the slope (m) is negative.

Front

What does it mean if a line is horizontal?

Back

A horizontal line has a slope of 0 and can be represented by the equation y = b, where b is the y-coordinate of any point on the line.

Front

What does it mean if a line is vertical?

Back

A vertical line has an undefined slope and can be represented by the equation x = a, where a is the x-coordinate of any point on the line.

Front

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

Back

To convert from slope-intercept form (y = mx + b) to standard form (Ax + By = C), rearrange the equation to get all terms on one side.

Front

What is the significance of the coefficients in the equation of a line?

Back

In the equation y = mx + b, 'm' indicates the slope (steepness) of the line, and 'b' indicates the y-intercept (where the line crosses the y-axis).