Write the Equation of the Line: Given two points

Front

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

Back

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

Front

How do you calculate the slope (m) 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 (b) represent in the equation of a line?

Back

The y-intercept (b) represents the point where the line crosses the y-axis.

Front

Given two points (x1, y1) and (x2, y2), how can you find the equation of the line?

Back

First, calculate the slope (m) using m = (y2 - y1) / (x2 - x1). Then, use one of the points to solve for b in the equation y = mx + b.

Front

What is the equation of a line that has a slope of 1 and passes through the point (0, 0)?

Back

The equation is y = 1x + 0, or simply y = x.

Front

If a line has a slope of -2 and a y-intercept of 3, what is its equation?

Back

The equation is y = -2x + 3.

Front

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

Back

A slope of 0 indicates a horizontal line, which means the y-value remains constant regardless of the x-value.

Front

What is the significance of an undefined slope in a linear equation?

Back

An undefined slope indicates a vertical line, which means the x-value remains constant regardless of the y-value.

Front

How do you convert the standard form of a linear equation (Ax + By = C) to slope-intercept form (y = mx + b)?

Back

To convert, solve for y: y = (-A/B)x + (C/B). Here, -A/B is the slope (m) and C/B is the y-intercept (b).

Front

What is the equation of the line that passes through the points (1, 2) and (3, 4)?

Back

First, calculate the slope: m = (4 - 2) / (3 - 1) = 1. Then, using point (1, 2): y = 1x + 1.