Write the Equation of the Line

Front

What is the definition of the slope of a line?

Back

The slope of a line is a measure of its steepness, typically 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

How do you find the y-intercept of a line from its equation?

Back

The y-intercept of a line is the value of y when x is 0. In the equation y = mx + b, the y-intercept is represented by 'b'.

Front

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

Back

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

Front

How can you determine the equation of a line given a slope and a y-intercept?

Back

You can determine the equation of a line by using the slope-intercept form: y = mx + b, substituting 'm' with the slope and 'b' with the y-intercept.

Front

What does a positive slope indicate about a line?

Back

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

Front

What does a negative slope indicate about a line?

Back

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

Front

How do you write an equation for a line given two points?

Back

To write an equation for a line given two points (x1, y1) and (x2, y2), first calculate the slope (m) using 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 y - y1 = m(x - x1), where (x1, y1) is a point on the line and 'm' is the slope.

Front

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

Back

To convert from point-slope form (y - y1 = m(x - x1)) to slope-intercept form (y = mx + b), solve for y to isolate it on one side.

Front

What is the significance of the y-intercept in real-world applications?

Back

The y-intercept often represents the starting value or initial condition in real-world applications, such as costs or quantities before any changes occur.