Understanding Linear Equations and Slopes

This lesson, led by Mrs. Apia, covers graphs of linear equations in two variables. Students learn to write the equation of a line given two points or the slope and a point. The lesson includes finding the slope and y-intercept, using examples to illustrate these concepts. The point-slope and slope-intercept forms are explained, and exercises are provided to practice determining the equation of a line. The lesson concludes with a summary of key concepts.

What is one of the main objectives of this lesson?

• To write the equation of a line given two points

• To calculate the area of a triangle

• To understand the properties of circles

• To learn how to solve quadratic equations

How do you calculate the slope of a line given two points?

• By dividing the y-coordinates

• By multiplying the x and y coordinates

• By adding the x-coordinates

• By subtracting the y-coordinates and dividing by the difference in x-coordinates

What is the slope of a line if the points are (-2, 2) and (5, 4)?

• 5/3

• 1/2

• 3/5

• 2/7

What is the y-intercept of the line with slope 2/7 passing through the point (-2, 2)?

• 1 and 5/7

• 3 and 1/7

• 4 and 2/7

• 2 and 4/7

How is the equation of a line transformed into standard form?

• By dividing all terms by the slope

• By subtracting the y-intercept from both sides

• By ensuring all coefficients are integers and rearranging terms

• By adding the slope to both sides

What is the standard form of the equation y = -3/5x + 17/5?

• 3x + 5y = 17

• 5x + 3y = 17

• 5x - 3y = 17

• 3x - 5y = 17

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

• y = mx + b

• ax + by = c

• x/y = m

• m(x - x1) = y - y1

What information is needed to write the equation of a line?

• The radius and diameter of a circle

• Two points or one point and the slope

• The length and width of a rectangle

• The area and perimeter of a shape

What is the slope-intercept form of a line?

• ax + by = c

• y = mx + b

• x = my + b

• y = ax + c

What must you memorize to effectively write the equation of a line?

• The quadratic formula

• The Pythagorean theorem

• The slope and y-intercept formulas

• The formula for the area of a circle