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 slope represent in a linear equation?

Back

Slope represents the steepness of the line and the direction it goes. It is calculated as the change in y divided by the change in x (rise over run).

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 find the y-intercept of a line?

Back

To find the y-intercept, set x = 0 in the equation of the line and solve for y.

Front

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

Back

The y-intercept is 4.

Front

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

Back

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

Front

How do you convert from point-slope form to slope-intercept form?

Back

Distribute the slope and then isolate y to get it into the form y = mx + b.

Front

What is the formula to calculate the slope between two points (x1, y1) and (x2, y2)?

Back

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

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.