Linear Equations and Their Forms

This lesson continues from the previous one, focusing on writing equations of a line. It covers finding the slope using two points, using the slope-intercept form, converting to standard form, and exploring proportional relationships. The lesson includes examples and exercises to reinforce these concepts.

What is the primary focus of this lesson?

• Solving inequalities

• Writing equations of a line

• Graphing parabolas

• Understanding quadratic equations

When given two points on a line, what is the first step to find the equation of the line?

• Convert to standard form

• Graph the points

• Calculate the slope

• Find the y-intercept

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

• Add the slope to both sides

• Rearrange terms to eliminate fractions

• Divide by the x-coordinate

• Multiply by the y-intercept

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

• Solving systems of equations

• Writing an equation with a given point and slope

• Graphing quadratic functions

• Finding the y-intercept directly

Which form of a linear equation is used when the line passes through the origin?

• Quadratic form

• Standard form

• Slope-intercept form

• Point-slope form

What is the slope of a line that passes through the points (5, 4) and (-2, 2)?

• 1/3

• 7/2

• 3/1

• 2/7

In the point-slope form, what does the 'm' represent?

• The y-intercept

• The slope

• The constant term

• The x-coordinate

What is the y-intercept of the line with the equation y = 5x - 58?

• 58

• 5

• -58

• 0

Which of the following is a characteristic of a proportional relationship?

• It forms a parabola

• It has a constant y-intercept

• It passes through the origin

• It has a variable slope

What is the standard form of the equation y = 4x - 29?

• 4x - y = 29

• y - 4x = 29

• 4x + y = 29

• y = 4x + 29