Graphing Linear Equations

What is the definition of slope in a linear equation?

• The slope is a measure of the steepness of a line, represented as the ratio of the rise (change in y) over the run (change in x).

• The slope is the point where the line intersects the y-axis.

• The slope is the distance between two points on the line.

• The slope is the angle formed by the line with the x-axis.

How do you graph a linear equation in slope-intercept form?

• Start at the x-intercept (a) on the x-axis, then use the slope (m) to determine the rise over run.

• Start at the y-intercept (b) on the y-axis, then use the slope (m) to determine the rise over run.

• Plot random points on the graph and connect them with a line.

• Use the slope (m) to find the x-intercept (a) and plot it on the graph.

How can you determine the equation of a line given its slope and a point on the line?

• You can use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

• You can use the slope-intercept form: y = mx + b, where b is the y-intercept.

• You can use the standard form: Ax + By = C, where A, B, and C are constants.

• You can use the quadratic formula to find the equation of the line.

What is the relationship between perpendicular lines in terms of slope?

• Perpendicular lines have slopes that are equal to each other (m1 = m2).

• Perpendicular lines have slopes that are negative reciprocals of each other (m1 * m2 = -1).

• Perpendicular lines have slopes that add up to zero (m1 + m2 = 0).

• Perpendicular lines have slopes that are both positive (m1 > 0 and m2 > 0).

What does a negative slope indicate about a linear relationship?

• A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the line.

• A negative slope indicates that as x increases, y increases, resulting in an upward slant of the line.

• A negative slope indicates that there is no relationship between x and y.

• A negative slope indicates that y remains constant as x changes.

What is the significance of the equation y = 0?

• It represents the y-axis, where all points have a y-coordinate of zero.

• It represents the x-axis, where all points have a y-coordinate of zero.

• It represents a horizontal line at y = 1.

• It represents a vertical line at x = 0.

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

• y = mx + b

• y = bx + m

• y = mx - b

• y = b - mx

What is the relationship between parallel lines in terms of slope?

• Parallel lines have different slopes.

• Parallel lines have the same slope but different y-intercepts.

• Parallel lines intersect at a right angle.

• Parallel lines have the same y-intercept.

What does the term 'linear equation' refer to?

• An equation that represents a straight line when graphed, typically in the form y = mx + b.

• An equation that represents a curve when graphed, typically in the form y = ax^2 + bx + c.

• An equation that has no solutions and does not intersect the x-axis.

• An equation that represents a circle when graphed, typically in the form (x-h)^2 + (y-k)^2 = r^2.

What is the significance of a positive slope?

• A positive slope indicates that as x increases, y also increases, resulting in an upward slant of the line.

• A positive slope indicates that as x increases, y decreases, resulting in a downward slant of the line.

• A positive slope indicates that there is no relationship between x and y.

• A positive slope indicates that y remains constant regardless of the value of x.