Identify Linear Equations & graphs

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 from 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 of the line represented by the equation y = -2x + 3?

Back

The slope of the line is -2.

Front

What is the y-intercept in the equation y = 4x - 1?

Back

The y-intercept is -1, which is the point where the line crosses the y-axis.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, meaning the line goes downwards from left to right.

Front

Complete the table for the function f(x) = 2x - 5 when x = 0.

Back

f(0) = 2(0) - 5 = -5.

Front

What is the slope-intercept form of the equation 3x + 2y = 6?

Back

The slope-intercept form is y = -rac{3}{2}x + 3.

Front

How do you convert the standard form of a linear equation to slope-intercept form?

Back

To convert, solve for y in terms of x (y = mx + b).

Front

What is the equation of a line with a slope of 1 and a y-intercept of -2?

Back

The equation is y = 1x - 2 or simply y = x - 2.