Understanding the Equation of a Line

Mrs. A explains how to find the equation of a line given two points. The process involves calculating the slope using the slope formula and then finding the y-intercept by substituting one of the points into the equation. A shortcut is also discussed, where recognizing a point with an x-coordinate of zero can directly give the y-intercept. The final equation is derived as y = -3/2x + 5.

What is the first step in finding the equation of a line given two points?

• Calculate the y-intercept

• Find the slope

• Plot the points on a graph

• Determine the midpoint

Which formula is used to calculate the slope of a line?

• a^2 + b^2 = c^2

• x1 + x2 / 2

• y = mx + b

• y2 - y1 / x2 - x1

What is the slope of the line passing through the points (4, -1) and (0, 5)?

• 1.5

• -1.5

• -3/2

• 3/2

Why is it beneficial to use reduced fractions for the slope?

• It makes calculations easier

• It clearly shows the rise and run

• It simplifies the y-intercept

• It helps in finding the midpoint

After finding the slope, what is the next step in determining the equation of the line?

• Draw the line on a graph

• Find the midpoint

• Check for parallel lines

• Calculate the y-intercept

How do you find the y-intercept using a point and the slope?

• Set x to zero in the equation

• Add the slope to the x-coordinate

• Use the formula y = mx + b

• Subtract the slope from the y-coordinate

What is the y-intercept of the line with the equation y = -3/2x + 5?

• -3/2

• 5

• 0

• -5

What is the final equation of the line passing through the points (4, -1) and (0, 5)?

• y = -3/2x - 5

• y = 3/2x - 5

• y = -3/2x + 5

• y = 3/2x + 5

What is a quick way to identify the y-intercept if one of the points has an x-coordinate of zero?

• The y-coordinate of that point is the y-intercept

• The slope is the y-intercept

• The midpoint is the y-intercept

• The x-coordinate of that point is the y-intercept

What is the significance of the point (0, 5) in the context of the line equation?

• It is the slope

• It is the y-intercept

• It is the x-intercept

• It is the midpoint