writing linear equations

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 of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive slope means it rises, negative slope means it falls).

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 of 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

Write the equation of a line with a slope of 3 that passes through the point (1, 2).

Back

y = 3x - 1.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.

Front

Write the equation of a line that is parallel to y = 4x + 1 and passes through the point (2, 3).

Back

y = 4x - 5.

Front

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

Back

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

Front

Convert the equation y = -2x + 3 to slope-intercept form.

Back

The equation is already in slope-intercept form: y = mx + b.

Front

How do you determine if a point (x, y) lies on a line represented by an equation?

Back

Substitute the x-value into the equation and see if the resulting y-value matches the y-value of the point.