The problem asks to find the $x$-intercept of the line $y = 3x - 6$.

AlgebraLinear Equationsx-interceptCoordinate Geometry
2025/3/28

1. Problem Description

The problem asks to find the xx-intercept of the line y=3x6y = 3x - 6.

2. Solution Steps

The xx-intercept is the point where the line crosses the xx-axis. At this point, the yy-coordinate is

0. So, to find the $x$-intercept, we set $y = 0$ in the equation $y = 3x - 6$ and solve for $x$.

0=3x60 = 3x - 6
Add 6 to both sides:
6=3x6 = 3x
Divide both sides by 3:
x=63x = \frac{6}{3}
x=2x = 2
So, the xx-intercept is
2.

3. Final Answer

The xx-intercept of the line y=3x6y = 3x - 6 is 2.

Related problems in "Algebra"

The problem consists of three exercises. Exercise 1 asks to determine the domain of definition of so...

FunctionsDomainParityTrigonometryTrigonometric EquationsTrigonometric Inequalities
2025/5/6

We are given the function $f(x) = (x-a)^2(x-b)^2$ and we need to find the value of $f(a+b)$.

FunctionsPolynomialsSubstitution
2025/5/6

We are given the function $f(x) = x^2 - 3x + 4$. We want to find the values of $x$ such that $f(x) =...

Quadratic EquationsFunctionsEquation SolvingAlgebraic Manipulation
2025/5/6

The problem is to solve question 13: If $f(x) = x^3$, find the value of $\frac{f(5) - f(1)}{5-1}$.

FunctionsPolynomialsEvaluation
2025/5/6

We are given a system of two equations: $x^2 + y^2 = 40$ $x^2 - y^2 = 10$ We need to solve for $x$ a...

Systems of EquationsQuadratic EquationsSolving Equations
2025/5/6

The problem consists of multiple parts. We need to solve the problems from question 7 to 13 from the...

FunctionsFunction EvaluationFunction PropertiesTrigonometric Identities
2025/5/6

We are given the function $f(x) = \frac{x-1}{x+1}$. We need to prove that $f(2x) = \frac{3f(x)+1}{f(...

Function PropertiesFunction CompositionAlgebraic Manipulation
2025/5/6

The problem is to solve the equation $0 - 4 = \frac{1}{4}y$ for $y$.

Linear EquationsSolving Equations
2025/5/6

We are given the equation $0-4 = -\frac{1}{4}^y$ and we want to solve for $y$.

ExponentsEquationsSolving EquationsAlgebraic Manipulation
2025/5/6

The problem asks us to find $f(x-1)$ given the function $f(x) = 3x^4 - 5x^2 + 9$.

PolynomialsFunction TransformationAlgebraic ManipulationSubstitution
2025/5/6