what is the graph of a linear inequality in one variable?
431277
The graph of a linear inequality in one variable is a number line. Use an open circle for < and > and a closed circle for ≤ and ≥. Inequalities that have the same solution are called equivalent.
1210475
The function inside the absolute value, 2x+1, is linear, so the graph is composed of straight lines. The graph of \begin{align*}y=|2x^2-1|\end{align*} is curved, and it does not have a single vertex, but two “cusps.” The function inside the absolute value is NOT linear, therefore the graph contains curves.
1147665
['If b = 0 in a linear equation (so y = mx), then the equation is a proportional linear relationship between y and x.', 'If b ≠ 0, then y = mx + b is a non-proportional linear relationship between y and x.']
197361
When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function. If the constant is greater than 1, we get a vertical stretch; if the constant is between 0 and 1, we get a vertical compression.
545531
the graph of the linear inequality 2 x-3 y<12 is a straight line passing through the point (6,0) and (0,-4) such that the line is dotted since the inequality is strict and the shaded region lie towards the origin.
1448546
['The graph passes through the point (0,1)', 'The domain is all real numbers.', 'The range is y>0.', 'The graph is increasing.', 'The graph is asymptotic to the x-axis as x approaches negative infinity.']
786075
If the graph is a straight line having a slope that is neither zero nor infinity, the relationship between the variables is proportional; (2) Inspect the equation to see if it has (or can be made to have) the form y = kx, or x = ky, where k is a constant.
117948
The graph of linear inequalities include a dashed line if they are greater than or less than but not equal to. Linear equations, on the other hand, include a solid line in every situation. Moreover, linear inequalities include shaded regions whereas linear equations do not.
1056404
If the inequality is < or >, graph the equation as a dotted line. If the inequality is ≤ or ≥, graph the equation as a solid line. This line divides the xy- plane into two regions: a region that satisfies the inequality, and a region that does not.
106367
A linear function is one of the form y = mx + c. For each input of x, you get one output for y. The graph of these functions is a single straight line. A quadratic function is one of the form y = ax2 + bx + c.
805887
Inequalities are the relationships between two expressions which are not equal to one another. The symbols used for inequalities are <, >, ≤, ≥ and ≠. reads as '7 is greater than ' (or ' is less than 7', reading from right to left).
61829
While all linear equations produce straight lines when graphed, not all linear equations produce linear functions. In order to be a linear function, a graph must be both linear (a straight line) and a function (matching each x-value to only one y-value).
1475709
This is the graph of . ... Not quite; if we look really close at x = -1, we see a hole in the graph, called a point of discontinuity. The line just skips over -1, so the line isn't continuous at that point. It's not as dramatic a discontinuity as a vertical asymptote, though.
678828
The equation of a linear function has no exponents higher than 1, and the graph of a linear function is a straight line. The equation of a non-linear function has at least one exponent higher than 1, and the graph of a non-linear function is a curved line.
81517
['Look for the y-intercept where the graph crosses the y-axis.', 'Look for the x-intercept where the graph crosses the x-axis.', 'Look for the zeros of the linear function where the y-value is zero.']
65501
An absolute value inequality is an inequality that has an absolute value sign with a variable inside.
844862
Two quantities that are in direct proportion will always produce a straight-line graph that passes through the origin. If the constant of proportionality is positive, the graph will have a positive gradient. If the constant is negative, the graph will have a negative gradient.