Writing Equations from Graphs

Front

What is the definition of slope in a linear equation?

Back

The slope is a measure of the steepness of a line, represented as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

How do you find the slope from a graph?

Back

To find the slope from a graph, select two points on the line, determine the rise (change in y) and run (change in x) between these points, and then calculate the slope using the formula: slope = rise/run.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as the value of y when x = 0.

Front

How can you determine the y-intercept from a graph?

Back

The y-intercept can be determined by locating the point where the line intersects the y-axis.

Front

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

Back

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

Front

How do you write the equation of a line given its slope and y-intercept?

Back

To write the equation of a line, use the slope-intercept form y = mx + b, substituting m with the slope and b with the y-intercept.

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal, meaning there is no vertical change as x changes.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that the line is decreasing, meaning as x increases, y decreases.

Front

How do you convert a slope from a fraction to a decimal?

Back

To convert a slope from a fraction to a decimal, divide the numerator by the denominator.

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent rates of change in real-world contexts, such as speed, cost per item, or growth rates.