-1
3
There are no common points for the following two equations: y = 2x + 3 y = 2x - 1 If you graph the two lines, since they have the same slope, they are parallel - they will never cross.
-1
As stated these are not lines, but just a collection of algebraic terms. If we change them to y=2x and y=2x-1, then on a graph of y versus x, these are parallel lines separated by vertical distance of 1.
5
-4
The graph of an inequality in the coordinate plane represents a region that satisfies the inequality. For example, the inequality (y < 2x + 3) would be graphed by first drawing the line (y = 2x + 3) as a dashed line (indicating that points on the line are not included), and then shading the area below the line, which contains all the points that satisfy the inequality. The boundary line can be solid if the inequality is "less than or equal to" or "greater than or equal to."
You can do the equation Y 2x plus 3 on a graph. On this graph the Y would equal 5 and X would equal to 0.
3
Graphing inequalities on a grid involves first translating the inequality into an equation to determine the boundary line. For example, for the inequality (y < 2x + 3), you would graph the line (y = 2x + 3) as a dashed line (indicating that points on the line are not included). Next, you select a test point (usually the origin, if it’s not on the line) to determine which side of the line to shade. The shaded region represents all the solutions to the inequality.
2x plus y = -3 (subtract 2x from both sides) y = -2x - 3 slope = -2 y-intercept = -3
The inequality ( y - 2 < 2(x - 1) ) can be rewritten as ( y < 2x - 2 + 2 ), simplifying to ( y < 2x ). This represents a region below the line ( y = 2x ) in a Cartesian plane. The line itself is not included in the solution, so it would be drawn as a dashed line. The area below this line, where ( y ) values are less than ( 2x ), indicates the solution set for the inequality.
3
To write the slope-intercept inequality for a graph, first identify the slope (m) and y-intercept (b) from the line. If the line is dashed, the inequality will be either < or >, while a solid line indicates ≤ or ≥. For example, if the line has a slope of 2 and a y-intercept of 3, the inequality could be y < 2x + 3 if the region below the line is shaded. Be sure to adjust the inequality symbol based on the line type and the shaded area.
To determine the inequality represented by the graph, we need to analyze the lines and their slopes. If the line has a positive slope and the region above the line is shaded, it likely corresponds to option (1) or (3). If the line has a negative slope and the region below the line is shaded, it corresponds to option (2) or (4). Without seeing the graph, I can't specify which inequality it is, but you can use these clues to identify the correct option.
y - 2x < 2
y=-2x^2+8x+3