Slope Intercept Form

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 determine the slope from two points (x1, y1) and (x2, y2)?

Back

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

Front

What does the slope of a line represent in a graph?

Back

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

Front

What is the y-intercept in the slope-intercept form?

Back

The y-intercept (b) is the point where the line crosses the y-axis, represented as (0, b).

Front

How can you find the equation of a line given a point and the slope?

Back

You can use the point-slope form of the equation, which is y - y1 = m(x - x1), and then rearrange it to slope-intercept form.

Front

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

Back

The point-slope form is given by 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, solve for y: y = m(x - x1) + y1, which simplifies to y = mx + (y1 - mx1).

Front

What is the significance of a positive slope?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant of the line.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the line.

Front

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

Back

First, calculate the slope using the two points, then use one of the points and the slope to write the equation in point-slope form, and convert it to slope-intercept form.