Linear Equations

What is the definition of an intercept in the context of a line on a coordinate plane?

An intercept is the point where a line crosses an axis.

What is the y-intercept of a line?

The point where the line crosses the y-axis, with coordinates (0, y).

How do you find the y-intercept of a line?

Substitute x=0 into the equation of the line and solve for y.

What is the x-intercept of a line?

The point where the line crosses the x-axis, with coordinates (x, 0).

How do you find the x-intercept of a line?

Substitute y=0 into the equation of the line and solve for x.

What does slope measure in relation to a line?

Slope measures the steepness and direction of the line.

What is the formula used to calculate the slope of a line?

m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are points on the line.

What does a positive slope indicate?

The line rises as you move from left to right.

What does a negative slope indicate?

The line falls as you move from left to right.

What does a zero slope indicate?

The line is horizontal.

What does an undefined slope indicate?

The line is vertical.

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

y = mx + b, where m is the slope and b is the y-intercept.

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

y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.