Finding Equations of Lines

Front

What is the definition of slope in a linear equation?

Back

The slope of a line is a measure of its steepness, represented as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

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 calculate the slope between two points (x1, y1) and (x2, y2)?

Back

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

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 y when x = 0.

Front

Given the points (0, -2) and (-5, 3), find the slope of the line.

Back

The slope is m = (3 - (-2)) / (-5 - 0) = 5 / -5 = -1.

Front

Find the equation of the line that passes through the points (3, 3) and (1, -5).

Back

The equation is y = 4x - 9.

Front

What is the slope of the line represented by the equation y = 2x + 3?

Back

The slope is 2.

Front

Write the equation in slope-intercept form for the line through (4, -5) and (-4, -1).

Back

The equation is y = -\frac{1}{2}x - 3.

Front

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

Back

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

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that the line is decreasing, meaning as x increases, y decreases.