Slope, Intercepts, and Line Equations

This video tutorial covers unit six lesson nine practice problems, focusing on equations of lines and parabolas. It explains point-slope, slope-intercept, and standard forms, and how to verify if points lie on a line. The video also discusses parabolas with a focus and directrix, and how to find the center of a circle using completing the square. Finally, it demonstrates reflecting and translating points on a graph.

What is the first step in writing the equation of a line?

• Identify the y-intercept

• Find the midpoint

• Calculate the slope

• Determine the x-intercept

Which form of a line equation uses the format y - y1 = m(x - x1)?

• Quadratic form

• Point-slope form

• Standard form

• Slope-intercept form

What is the y-intercept in the equation y = 3/2x - 3?

• 3

• 0

• 3/2

• -3

How do you convert y = 3/2x - 3 to standard form?

• Multiply by 3

• Add 3 to both sides

• Multiply by 2

• Subtract x from both sides

What is the x-intercept of the equation 3x - 2y = 6?

• 6

• 2

• 0

• 3

Why is the point (3, 6) on the line with slope 3/2?

• The slope between points is 3/2

• It is the y-intercept

• It is the x-intercept

• It is the midpoint

What is the slope between points (13, 22) and (1, 3)?

• 1/2

• 22/13

• 19/12

• 3/2

How do you write the equation of a line through (3, 5) with slope 4?

• y - 5 = 4(x - 3)

• y = 4x + 3

• y = 3x + 4

• y - 3 = 5(x - 4)

What is the distance from a point on a parabola to its directrix?

• Half the distance to the focus

• Twice the distance to the focus

• Unrelated to the focus

• Equal to the distance to the focus

How do you find the equation of a parabola with a focus at (3, -2) and directrix y = 2?

• Use the midpoint formula

• Use the slope formula

• Use the distance formula

• Use the Pythagorean theorem