Review 12-16-24

Front

What is a function?

Back

A relation where each input (x-value) has exactly one output (y-value).

Front

Is the relation {(1,2), (1,3), (2,4)} a function? Why?

Back

No, because the x-value 1 has two y-values (2 and 3).

Front

What does it mean for a system of linear equations to have no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

Front

Write the point-slope form of the equation for a line through the point (3, 2) with a slope of 4.

Back

y - 2 = 4(x - 3).

Front

What is the x-intercept of a line?

Back

The point where the line crosses the x-axis, where y = 0.

Front

How do you find the x-intercept of the equation 2x + 3y = 6?

Back

Set y = 0 and solve for x: 2x = 6, so x = 3. The x-intercept is (3, 0).

Front

What is the slope of a line parallel to y = 2x + 5?

Back

The slope is 2, as parallel lines have the same slope.

Front

Write the equation of a line in slope-intercept form that is parallel to y = 3x - 1 and passes through (1, 2).

Back

y = 3x - 1.

Front

What is the point-slope form of a line?

Back

An equation of the form y - y_1 = m(x - x_1), where m is the slope and (x_1, y_1) is a point on the line.

Front

How do you determine if two lines are parallel?

Back

If their slopes are equal, the lines are parallel.