slope intercept form

Front

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

Back

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

Front

How do you find the slope (m) of a line given two points (x1, y1) and (x2, y2)?

Back

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

Front

What does the y-intercept (b) represent in the slope-intercept form?

Back

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

Front

If a line has a slope of 4, what does this indicate about the line's steepness?

Back

A slope of 4 indicates that for every 1 unit increase in x, y increases by 4 units, making the line steep.

Front

Write the equation of the line in slope-intercept form with slope m = 2 and y-intercept b = 3.

Back

y = 2x + 3.

Front

What is the slope of the line represented by the equation y = -3x + 5?

Back

The slope of the line is -3.

Front

How do you convert the standard form of a linear equation (Ax + By = C) to slope-intercept form?

Back

To convert, solve for y to isolate it on one side: y = (-A/B)x + (C/B).

Front

What is the y-intercept of the line represented by the equation y = 1/2x - 4?

Back

The y-intercept is -4.

Front

If a line has a slope of 0, what type of line is it?

Back

A line with a slope of 0 is a horizontal line.

Front

What is the significance of a negative slope in a linear equation?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant from left to right.