Identifying the Point of Intersection

Front

What is the point of intersection of two lines?

Back

The point of intersection is the point where two lines meet or cross each other on a graph, representing the solution to a system of equations.

Front

How do you find the point of intersection graphically?

Back

To find the point of intersection graphically, plot both lines on a coordinate plane and identify the coordinates of the point where they intersect.

Front

What does the slope-intercept form of a line look like?

Back

The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

If m=3 and b=6, what is the slope-intercept equation?

Back

y = 3x + 6

Front

What is the solution to the system of equations represented by the lines y = 2x + 1 and y = -x + 4?

Back

The solution is the point where the two lines intersect, which can be found by solving the equations simultaneously.

Front

What does it mean if two lines are parallel?

Back

If two lines are parallel, they never intersect and have the same slope but different y-intercepts.

Front

What does it mean if two lines are perpendicular?

Back

If two lines are perpendicular, they intersect at a right angle (90 degrees) and the product of their slopes is -1.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x is 0.

Front

How can you determine if a system of equations has no solution?

Back

A system of equations has no solution if the lines are parallel, meaning they have the same slope but different y-intercepts.

Front

What is the solution to the system of equations y = 3x + 2 and y = 3x - 4?

Back

The system has no solution because the lines are parallel.