Writing Equations of Lines with Slope and Point

The video tutorial introduces the point-slope form of linear equations, explaining how to write the equation of a line given a slope and a point. It provides multiple examples, demonstrating the conversion from point-slope form to slope-intercept form, and highlights common mistakes to avoid, such as handling negative coordinates.

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

• y = m(x + b)

• ax + by = c

• y - y1 = m(x - x1)

• y = mx + b

In the equation y - y1 = m(x - x1), what does 'm' represent?

• The slope of the line

• The y-coordinate of the point

• The x-coordinate of the point

• The y-intercept

What is the first step in converting a point-slope form equation to slope-intercept form?

• Distribute the slope to the terms inside the parentheses

• Add the y-coordinate to both sides

• Multiply both sides by the slope

• Subtract the x-coordinate from both sides

Given the point (4, 5) and a slope of 1/2, what is the point-slope form of the equation?

• y - 4 = 1/2(x - 5)

• y + 5 = 1/2(x + 4)

• y - 5 = 1/2(x - 4)

• y + 4 = 1/2(x + 5)

What is the slope-intercept form of the equation y - 5 = 1/2(x - 4)?

• y = 1/2x + 5

• y = 1/2x - 5

• y = 1/2x - 3

• y = 1/2x + 3

For the point (2, 2) and slope -3, what is the point-slope form of the equation?

• y + 2 = -3(x - 2)

• y + 2 = -3(x + 2)

• y - 2 = -3(x - 2)

• y - 2 = -3(x + 2)

What is the slope-intercept form of the equation y - 2 = -3(x - 2)?

• y = -3x + 8

• y = -3x - 8

• y = -3x - 6

• y = -3x + 6

For the point (-6, 2) and slope 1/2, what is the point-slope form of the equation?

• y - 2 = 1/2(x + 6)

• y + 2 = 1/2(x - 6)

• y - 2 = 1/2(x - 6)

• y + 2 = 1/2(x + 6)

What is the slope-intercept form of the equation y - 2 = 1/2(x + 6)?

• y = 1/2x - 3

• y = 1/2x + 5

• y = 1/2x - 5

• y = 1/2x + 3

For the point (12, -3) and slope 1/4, what is the slope-intercept form of the equation?

• y = 1/4x + 6

• y = 1/4x + 3

• y = 1/4x - 6

• y = 1/4x - 3