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 the line 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 slope-intercept form y = mx + b.

Front

Convert the point-slope form to slope-intercept form: y - y1 = m(x - x1).

Back

To convert to slope-intercept form, solve for y: y = mx - mx1 + y1.

Front

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

Back

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

Front

Write the equation of the line that goes through (-4, 1) and (2, 13) in slope-intercept form.

Back

y = 2x + 9.

Front

What is the equation of the line that has a slope of 5 and goes through the point (2,7)?

Back

y = 5x - 3.

Front

Given the table, write the equation in the slope-intercept form: y = 2x + 6.

Back

The equation represents a linear relationship where the slope is 2 and the y-intercept is 6.

Front

Which equation best represents the relationship between x and y in the table shown?

Back

y = 5x + 5.