Understanding Linear Equations and Graphs

The video tutorial covers graphing equations in both slope-intercept and standard forms. It explains how to convert standard form equations to slope-intercept form and graph them. The tutorial also demonstrates graphing horizontal and vertical lines, highlighting the differences in slopes. Finally, it discusses how to identify linear and nonlinear equations based on the presence of exponents.

What is the first step in graphing an equation in standard form?

• Find the x-intercept

• Plot random points

• Convert it to slope-intercept form

• Find the y-intercept

If an equation is in the form y = mx + b, what does 'b' represent?

• The slope

• The origin

• The y-intercept

• The x-intercept

How do you find the x-intercept of an equation in standard form?

• Graph the equation

• Use the slope formula

• Set x to 0 and solve for y

• Set y to 0 and solve for x

What is the y-intercept of the equation 3/4x + y = 8?

• 3/4

• 0

• 8

• 4

When graphing a line, what does a negative slope indicate?

• The line rises to the right

• The line is horizontal

• The line falls to the right

• The line is vertical

What is the slope of a horizontal line?

• Negative

• Undefined

• Zero

• Positive

What is the slope of a vertical line?

• Zero

• Positive

• Undefined

• Negative

Which of the following equations represents a horizontal line?

• x = 0

• y = 2x + 1

• y = 3

• x = 5

Why is the equation 4x + 5y = 3/7 considered linear?

• It has no exponents on variables

• It has a constant term

• It is in slope-intercept form

• It has a variable in the denominator

What makes an equation non-linear?

• Having no intercepts

• Having a slope of zero

• Being in standard form

• Having a variable with an exponent