U2 Equations and Inequalities Review

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

To convert to slope-intercept form, subtract $$2x$$ from both sides to isolate $$y$$ : $$4y = -2x + 8$$ , then divide by 4: $$y = -\frac{1}{2}x + 2$$ .

The slope represents the rate of change of $$y$$ with respect to $$x$$ , indicating how steep the line is.

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other.

To graph a linear inequality, first graph the corresponding equation as a line, then shade the region that satisfies the inequality.

A solid line indicates that points on the line are included in the solution (e.g., @@y eq 3x - 5 $$), while a dashed line indicates they are not included (e.g.,$$ y < 3x - 5@@).

The y-intercept is the point where the line crosses the y-axis, which is $$3$$ in this case.

To find the x-intercept, set $$y = 0$$ and solve for $$x$$ : $$0 = 2x + 3$$ , leading to $$x = -\frac{3}{2}$$ .

The standard form is given by $$Ax + By = C$$ , where $$A$$ , $$B$$ , and $$C$$ are integers.

The first step is to subtract $$b$$ from both sides: $$y - b = mx$$ .