Understanding Linear Equations

This video tutorial explains how to write the equation of a line given a slope and a point. It covers using the slope-intercept formula to find the y-intercept, converting the equation to standard form, and solving an example problem. Additionally, it demonstrates writing the equation in point-slope form, providing a comprehensive understanding of different forms of line equations.

What is the formula used to write the equation of a line when given a slope and a point?

• y = a + bx

• y = mx + b

• y = ax^2 + bx + c

• y = x^2 + 2x + 1

If the slope of a line is 3/2 and it passes through the point (4, -5), what is the y-intercept?

• -5

• 11

• -11

• 5

What is the equation of the line in slope-intercept form with a slope of 3/2 and y-intercept of -11?

• y = 3/2x - 11

• y = 2x - 3

• y = 2/3x + 11

• y = 3x + 2

How do you convert an equation from slope-intercept form to standard form?

• Add the slope to both sides

• Divide by the slope

• Multiply by a common factor to eliminate fractions and rearrange terms

• Subtract the y-intercept from both sides

What is the standard form of the equation y = 3/2x - 11?

• 3x + 2y = 11

• 2x + 3y = 11

• 2x - 3y = 22

• 3x - 2y = 22

In the new example, what is the slope of the line?

• -3/5

• 3/5

• 5/3

• -5/3

What is the y-intercept of the line passing through (-4, 3) with a slope of -5/3?

• 3/11

• -3/11

• 11/3

• -11/3

What is the standard form of the equation y = -5/3x - 11/3?

• 3x + 5y = -11

• 5x - 3y = 11

• 3x - 5y = 11

• 5x + 3y = -11

What is the point-slope form of the equation for a line with slope -5/3 passing through (-4, 3)?

• y + 3 = -5/3(x - 4)

• y - 3 = 5/3(x + 4)

• y + 3 = 5/3(x - 4)

• y - 3 = -5/3(x + 4)

Why is it useful to leave the equation in point-slope form?

• It simplifies to a quadratic equation

• It is easier to solve for y

• It clearly shows the slope and a point on the line

• It eliminates fractions