Slope and Y-Intercept

Front

What is the definition of slope in a linear equation?

Back

The slope (m) of a linear equation represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is and the direction it goes (positive or negative).

Front

How do you find the y-intercept of a linear equation?

Back

The y-intercept (b) of a linear equation is found by setting the value of x to 0 in the equation and solving for y. It represents the point where the line crosses 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 equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What does a positive slope indicate about a linear relationship?

Back

A positive slope indicates that as the independent variable (x) increases, the dependent variable (y) also increases, showing a direct relationship.

Front

What does a negative slope indicate about a linear relationship?

Back

A negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases, showing an inverse relationship.

Front

What is the significance of the y-intercept in a graph?

Back

The y-intercept is significant because it shows the starting value of the dependent variable (y) when the independent variable (x) is zero, providing context for the linear relationship.

Front

How can you determine the slope from two points on a line?

Back

The slope (m) can be determined using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is the relationship between slope and parallel lines?

Back

Parallel lines have the same slope. If two lines have equal slopes, they will never intersect and are therefore parallel.

Front

What is the relationship between slope and perpendicular lines?

Back

Perpendicular lines have slopes that are negative reciprocals of each other. If one line has a slope of m, the other will have a slope of -1/m.

Front

How do you convert a linear equation from standard form to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y to isolate it on one side of the equation.