Front

What is the definition of slope in a linear equation?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the equation of a line in slope-intercept form, y = mx + b. It is calculated as the change in y divided by the change in x (rise over run).

Front

How do you find the slope of a line given in standard form Ax + By = C?

Back

To find the slope from the standard form Ax + By = C, rearrange the equation into slope-intercept form (y = mx + b) by isolating y. The slope 'm' will be -A/B.

Front

What is the slope of a line parallel to another line?

Back

Lines that are parallel have the same slope. Therefore, the slope of any line parallel to a given line is equal to the slope of that line.

Front

What is the slope of the line 9x + 4y = 7?

Back

To find the slope, rearrange the equation into slope-intercept form: 4y = -9x + 7, which simplifies to y = -\frac{9}{4}x + \frac{7}{4}. The slope is -\frac{9}{4}.

Front

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

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the y-intercept represent in a linear equation?

Back

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

Front

How can you determine if two lines are parallel using their slopes?

Back

Two lines are parallel if their slopes are equal. If the slopes of two lines are the same, they will never intersect.

Front

What is the relationship between the slopes of perpendicular lines?

Back

The slopes of perpendicular lines are negative reciprocals of each other. If one line has a slope of m, the other line's slope will be -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, solve for y to isolate it on one side of the equation.

Front

What is the significance of the coefficients in a linear equation?

Back

The coefficients in a linear equation represent the slope and the y-intercept. The coefficient of x represents the slope, while the constant term represents the y-intercept.