The problem consists of two parts. Part 1: Given the function $f(x) = \frac{6x - 3}{5}$, find $f(1.2)$. Part 2: Find the slope and y-intercept of the line $2x + 7y = 14$.

AlgebraFunctionsLinear EquationsSlopeY-intercept
2025/5/2

1. Problem Description

The problem consists of two parts.
Part 1: Given the function f(x)=6x35f(x) = \frac{6x - 3}{5}, find f(1.2)f(1.2).
Part 2: Find the slope and y-intercept of the line 2x+7y=142x + 7y = 14.

2. Solution Steps

Part 1:
Substitute x=1.2x = 1.2 into the function f(x)f(x):
f(1.2)=6(1.2)35f(1.2) = \frac{6(1.2) - 3}{5}
f(1.2)=7.235f(1.2) = \frac{7.2 - 3}{5}
f(1.2)=4.25f(1.2) = \frac{4.2}{5}
f(1.2)=0.84f(1.2) = 0.84
Part 2:
Rewrite the equation 2x+7y=142x + 7y = 14 in the slope-intercept form y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.
7y=2x+147y = -2x + 14
y=27x+147y = \frac{-2}{7}x + \frac{14}{7}
y=27x+2y = \frac{-2}{7}x + 2
Thus, the slope is 27-\frac{2}{7} and the y-intercept is 22.

3. Final Answer

Part 1: f(1.2)=0.84f(1.2) = 0.84
Part 2: The slope is 27-\frac{2}{7} and the y-intercept is 22. So the answer is (b).

Related problems in "Algebra"

The problem describes a quadratic number pattern $4, p, 11, q, 22, ...$ with a constant second diffe...

SequencesQuadratic SequencesPatternsGeneral TermQuadratic Equations
2025/5/2

The problem asks us to solve the equation $\ln(x+2) + \ln(x) = \ln(x+30)$ for $x$.

LogarithmsEquationsQuadratic EquationsSolving EquationsAlgebraic Manipulation
2025/5/2

Pedro is 4 years older than Juan. Five times Juan's age is three times Pedro's age. What are their ...

Linear EquationsWord ProblemSystems of Equations
2025/5/2

We are given the following information about a triangle: - The longest side is 8 cm longer than side...

TrianglePerimeterLinear EquationsWord Problem
2025/5/2

The problem asks us to solve for $x$ in two equations: a) $\frac{a}{x} = \frac{b}{c}$ b) $\frac{ab}{...

EquationsSolving for xLinear EquationsCross-multiplication
2025/5/2

The problem provides the formula $\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2}$ and asks to solve f...

Equation SolvingFormula ManipulationReciprocals
2025/5/2

The problem consists of two parts. Part g) asks us to solve the equation $\frac{x}{5-y} = m-1$ for $...

Equation SolvingLinear EquationsVariable Isolation
2025/5/2

Solve the equation $\frac{2n}{x-4} = m$ for $x$.

Linear EquationsVariable SolvingEquation Manipulation
2025/5/2

Solve for $y$ in the equation $x+5 = \frac{3m}{y}$.

Equation SolvingAlgebraic ManipulationVariables
2025/5/2

We are given several equations and asked to isolate a specified variable in each. c) $\frac{ax}{y} =...

Equation SolvingVariable IsolationAlgebraic Manipulation
2025/5/2