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 identify the slope from the slope-intercept form?

Back

In the equation y = mx + b, the slope is represented by the coefficient m.

Front

What does the variable 'b' represent in the slope-intercept form?

Back

The variable 'b' represents the y-intercept, which is the point where the line crosses the y-axis.

Front

If a line has a slope of 2, what does this indicate about the line's steepness?

Back

A slope of 2 indicates that for every 1 unit increase in x, the value of y increases by 2 units, making the line relatively steep.

Front

How can you convert the standard form of a linear equation 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.

Front

What is the significance of a slope of 0?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.

Front

What does a negative slope indicate about the direction of a line?

Back

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

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

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

Front

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

Back

The slope of the line is -3.

Front

If a line passes through the point (2, 3) and has a slope of 1/2, what is the equation of the line in slope-intercept form?

Back

Using the point-slope form, the equation is y - 3 = (1/2)(x - 2), which simplifies to y = (1/2)x + 2.