Graphing equations in 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 identify the slope from the slope-intercept form?

Back

In the slope-intercept form y = mx + b, the slope is represented by the coefficient m.

Front

What does the y-intercept represent in a graph?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

If a line has a slope of -3, what does this indicate about its direction?

Back

A slope of -3 indicates that for every 1 unit increase in x, the value of y decreases by 3 units, meaning the line descends from left to right.

Front

How can you determine the y-intercept from the equation y = -3x?

Back

In the equation y = -3x, the y-intercept is 0, as there is no constant term added to the equation.

Front

What is the significance of a slope of 0 in a linear equation?

Back

A slope of 0 indicates a horizontal line, meaning that the value of y remains constant regardless of the value of x.

Front

How do you convert the equation y = 2/3x - 3 into slope-intercept form?

Back

The equation y = 2/3x - 3 is already in slope-intercept form, where the slope is 2/3 and the y-intercept is -3.

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

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

Back

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

Front

What is the graphical representation of the equation y = 3x + 2?

Back

The graph of y = 3x + 2 is a straight line with a slope of 3 and a y-intercept of 2.