Graphing Linear Equations and Intercepts

The video tutorial explains how to graph linear equations and determine the number of solutions for systems of equations. It covers finding x and y intercepts, graphing lines, and analyzing the solutions. The first system of equations results in infinite solutions as the lines coincide, while the second system has no solution due to parallel lines with different intercepts.

What is the first step in graphing a linear equation?

• Find the slope

• Determine the intercepts

• Plot random points

• Calculate the midpoint

How do you find the x-intercept of a linear equation?

• Solve for the slope

• Set y to zero and solve for x

• Set both x and y to zero

• Set x to zero and solve for y

What is the x-intercept of the first equation?

• (0, -4)

• (2, 0)

• (0, 4)

• (-2, 0)

What conclusion can be drawn when two lines have the same intercepts?

• They are parallel

• They are perpendicular

• They coincide

• They have no solution

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

• x = my + b

• y = ax + c

• y = mx + b

• ax + by = c

How do you determine the slope from the equation y = 1/3x - 1?

• The slope is 0

• The slope is 3

• The slope is -1

• The slope is 1/3

What is the y-intercept of the equation y = 1/3x - 1?

• 0

• -1

• 1

• 3

What does it mean if two lines have the same slope but different y-intercepts?

• They form a right angle

• They coincide

• They are parallel

• They intersect at one point

What is the y-intercept of the equation y = 1/3x?

• 3

• 0

• -1

• 1

What is the solution to a system of equations if the lines are parallel?

• Two solutions

• One solution

• Infinite solutions

• No solution