Linear Equations Review

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear equation?

Back

The slope (m) represents the rate of change of the y-value with respect to the x-value. It indicates how steep the line is and the direction it goes (positive or negative).

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

Front

What is point-slope form of a linear equation?

Back

Point-slope form is an equation of a line that passes through a given point (x1, y1) with a slope m, expressed as y - y1 = m(x - x1).

Front

Convert the point-slope form y - 7 = 3(x - 1) to slope-intercept form.

Back

To convert to slope-intercept form, expand and simplify: y - 7 = 3x - 3 => y = 3x + 4.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, resulting in an upward slant from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, resulting in a downward slant from left to right.

Front

What is the equation of a line that passes through the point (0, -9) with a slope of 16?

Back

The equation is y = 16x - 9.

Front

How do you write the equation of a line in slope-intercept form?

Back

To write the equation in slope-intercept form, use the formula y = mx + b, where m is the slope and b is the y-intercept.