Question

linear equations
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directions / instrucciones;
substitute the given values into each expression.
sustituye los valores dados en cada expresión.

1. substitute x = 2 into: 3x + 4
2. substitute (x = -1) into: 5 - 2x
3. substitute x = 4, y = -2 into: 2x - 3y

vocabulary / vocabulario
slope (m): the rate of change between x and y.
y - intercept (b): where the graph crosses the y - axis.
slope - intercept form: (y = mx + b )
standard form: (ax + by = c )
linear equation: an equation whose graph is a straight line.
pendiente (m): la tasa de cambio entre x y y.
intersección en y (b): donde la gráfica cruza el eje y.
forma pendiente - intersección: (y = mx + b )
forma estándar: (ax + by = c )
ecuación lineal: una ecuación cuya gráfica es una línea recta.
lesson objective: students will find intercepts, identify and write equations of parallel and perpendicular lines, and check if a point is a solution to an equation.
objetivo de la lección: los estudiantes hallarán intersecciones, identificarán y escribirán ecuaciones de líneas paralelas y perpendiculares, y verificarán si un punto es solución de una ecuación
standards: a - rei.3
section 1 — intercepts of linear equations
x - intercepts
y - intercepts

Explanation:

Problem 1: Substitute \( x = 2 \) into \( 3x + 4 \)

Step 1: Replace \( x \) with 2

Substitute \( x = 2 \) into the expression \( 3x + 4 \), we get \( 3(2) + 4 \).

Step 2: Calculate the result

First, calculate \( 3(2) = 6 \), then add 4: \( 6 + 4 = 10 \).

Step 1: Replace \( x \) with -1

Substitute \( x = -1 \) into the expression \( 5 - 2x \), we get \( 5 - 2(-1) \).

Step 2: Calculate the result

First, calculate \( 2(-1) = -2 \), then \( 5 - (-2) = 5 + 2 = 7 \) (because subtracting a negative is adding the positive).

Step 1: Replace \( x \) and \( y \)

Substitute \( x = 4 \) and \( y = -2 \) into the expression \( 2x - 3y \), we get \( 2(4) - 3(-2) \).

Step 2: Calculate each term

Calculate \( 2(4) = 8 \) and \( 3(-2) = -6 \), so the expression becomes \( 8 - (-6) \).

Step 3: Simplify the subtraction

\( 8 - (-6) = 8 + 6 = 14 \) (subtracting a negative is adding the positive).

Answer:

10

Problem 2: Substitute \( x = -1 \) into \( 5 - 2x \)