Understanding Linear Equations and Slopes

The video tutorial covers the basics of coordinate geometry, explaining how to describe points on a Cartesian plane using coordinates. It introduces the concept of equations representing lines, focusing on the gradient and y-intercept. The tutorial details the process of finding x and y intercepts and calculating the gradient using rise over run. It introduces the slope-intercept form (y=mx+b) as an efficient method to find the gradient and y-intercept without drawing. The video also demonstrates rearranging equations to this form and applies it to analyze line equations.

What are the coordinates of a point that is 3 units to the right and 4 units up from the origin?

• (3, 4)

• (0, 0)

• (4, 3)

• (-3, -4)

What does the y-intercept of a line represent?

• Where the line crosses the y-axis

• Where the line crosses the x-axis

• The slope of the line

• The midpoint of the line

To find the x-intercept of a line, what value should y be set to?

• The slope of the line

• 1

• 0

• x

If the equation of a line is 5x - 2y + 10 = 0, what is the x-intercept?

• 2

• -5

• -2

• 5

What is the y-intercept of the equation 5x - 2y + 10 = 0?

• 2

• -5

• 5

• -2

How is the gradient of a line determined using a right-angle triangle?

• By using the Pythagorean theorem

• By measuring the hypotenuse

• By calculating rise over run

• By finding the midpoint

What is the gradient of a line if the rise is 5 and the run is 2?

• 0.4

• 10

• 5

• 2.5

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

• y = ax^2 + bx + c

• ax + by = c

• x = my + b

• y = mx + b

In the slope-intercept form y = mx + b, what does 'm' represent?

• The slope

• The midpoint

• The x-intercept

• The y-intercept

If a line has a slope of -4 and a y-intercept of 2, what is its equation in slope-intercept form?

• y = -4x + 2

• y = -2x + 4

• y = 4x - 2

• y = 2x - 4