Algebra 1_ Fall Semester Review

Front

What is the equation of a line given a point and a slope?

Back

The equation of a line can be expressed in point-slope form: \(y - y_1 = m(x - x_1)\), where \(m\) is the slope and \((x_1, y_1)\) is a point on the line.

Front

How do you find the slope of a line from two points?

Back

The slope \(m\) of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated as \(m = \frac{y_2 - y_1}{x_2 - x_1}\).

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Front

What does it mean to translate a graph vertically?

Back

Translating a graph vertically means shifting it up or down without changing its shape. For example, adding a constant \(k\) to the function \(f(x)\) results in the new function \(f(x) + k\).

Front

How do you determine the new equation after translating a line?

Back

To find the new equation after translating a line vertically, add the translation value to the y-intercept of the original equation.

Front

What is the formula for the perimeter of a rectangle?

Back

The perimeter \(P\) of a rectangle is given by the formula \(P = 2(l + w)\), where \(l\) is the length and \(w\) is the width.

Front

How do you express the relationship between length and width in a rectangle?

Back

If the length \(l\) is 3 meters more than twice the width \(w\), it can be expressed as: \(l = 2w + 3\).

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as \(f(x)\) where \(x\) is the input.

Front

How do you find the total height of a building with multiple floors?

Back

The total height \(h(n)\) of a building with \(n\) floors, each of height \(h_f\), plus an additional height \(h_a\) (like an antenna), is given by: \(h(n) = h_f \cdot n + h_a\).

Front

What is the significance of the y-intercept in a linear equation?

Back

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