Finding Slope and Line Equations

Front

What is the point-slope form of a line?

Back

The point-slope form of a line is given by the equation: (y - y_1) = m(x - x_1), where (x_1, y_1) is a point on the line and m is the slope.

Front

How do you find the slope of a line given two points (x_1, y_1) and (x_2, y_2)?

Back

The slope (m) is calculated using the formula: m = (y_2 - y_1) / (x_2 - x_1).

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

How do you convert the equation of a line from point-slope form to slope-intercept form?

Back

To convert from point-slope form (y - y_1 = m(x - x_1)) to slope-intercept form (y = mx + b), solve for y.

Front

What is the slope-intercept form of a line?

Back

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

Front

If a line has a slope of 2, what is the slope of a line perpendicular to it?

Back

The slope of a line perpendicular to another line is the negative reciprocal. Therefore, if the slope is 2, the perpendicular slope is -1/2.

Front

How do you find the y-intercept of a line given its equation in slope-intercept form?

Back

In the slope-intercept form y = mx + b, the y-intercept is the value of b.

Front

What is the significance of the slope in a real-world context?

Back

The slope represents the rate of change; for example, in a distance-time graph, the slope indicates speed.