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).

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