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 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 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

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the slope-intercept form.

Front

Write the equation of a line with a slope of 3 that passes through the point (0, 2).

Back

y = 3x + 2.

Front

What is the equation of a line with a slope of -2 that passes through the point (1, 4)?

Back

y = -2x + 6.

Front

How do you convert a point-slope equation to slope-intercept form?

Back

Start with the point-slope form y - y1 = m(x - x1) and solve for y to get it into the form y = mx + b.

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

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

Back

y - 3 = 1/2(x - 2) or y = 1/2x + 2.