Writing Linear Equations Given a Point and Slope

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 y with respect to x. It indicates how steep the line is and the direction it goes (positive slope goes up, negative slope goes down).

Front

How do you find the y-intercept (b) of a linear equation?

Back

The y-intercept (b) is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

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

Back

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

Front

How do you write the equation of a line given a point and a slope?

Back

Use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.

Front

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

Back

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

Front

If a line has a slope of -2 and passes through the point (-1, 3), what is the equation of the line?

Back

Using point-slope form: y - 3 = -2(x + 1) simplifies to y = -2x + 1.

Front

What is the y-intercept of the line with the equation y = 3x + 4?

Back

The y-intercept is 4, which is the value of y when x = 0.

Front

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

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of the line that has a slope of 1/2 and passes through the point (2, 0)?

Back

Using the point-slope form: y - 0 = 1/2(x - 2) simplifies to y = 1/2x - 1, so the y-intercept is -1.