Semester Exam Review Part 1

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

A relation is a function if no two ordered pairs have the same first element (input).

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

The slope of a line represents the rate of change of the y-value with respect to the x-value; it indicates how steep the line is.

The y-intercept is the point where the line crosses the y-axis, represented by the value of $$b$$ in the slope-intercept form $$y = mx + b$$ .

To find the equation of a line given two points, calculate the slope using $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ and then use the point-slope form $$y - y_1 = m(x - x_1)$$ .

The total capacity can be expressed as $$4c + 8v = 44$$ , where $$c$$ is the number of cars and $$v$$ is the number of vans.

Identify the variables, write equations based on the relationships described in the problem, and include any constraints.

The solution is $$c = 3$$ (cars) and $$v = 4$$ (vans).

A linear equation is an equation that forms a straight line when graphed, typically in the form $$y = mx + b$$ .