Question

here is a system of equations.
\

$$\begin{cases} y = \\frac{1}{4}x - 1 \\ y = -3x + 4 \\end{cases}$$

your answer
(a) graph the system.

Explanation:

Step1: Find intercepts for $y=\frac{1}{4}x-1$

x-intercept: Set $y=0$, solve $0=\frac{1}{4}x-1$ → $x=4$, so point $(4,0)$.
y-intercept: Set $x=0$, $y=-1$, so point $(0,-1)$.

Step2: Find intercepts for $y=-3x+4$

x-intercept: Set $y=0$, solve $0=-3x+4$ → $x=\frac{4}{3}\approx1.33$, so point $(\frac{4}{3},0)$.
y-intercept: Set $x=0$, $y=4$, so point $(0,4)$.

Step3: Plot and connect points

For $y=\frac{1}{4}x-1$: Plot $(4,0)$ and $(0,-1)$, draw a straight line through them.
For $y=-3x+4$: Plot $(\frac{4}{3},0)$ and $(0,4)$, draw a straight line through them.

Step4: Find intersection (verify algebraically)

Set $\frac{1}{4}x-1=-3x+4$
$\frac{1}{4}x+3x=4+1$
$\frac{13}{4}x=5$
$x=\frac{20}{13}\approx1.54$
Substitute $x=\frac{20}{13}$ into $y=-3x+4$:
$y=-3\times\frac{20}{13}+4=\frac{-60+52}{13}=-\frac{8}{13}\approx-0.62$
Intersection point: $(\frac{20}{13}, -\frac{8}{13})$

Answer:

1. For $y=\frac{1}{4}x-1$: Plot points $(4, 0)$ and $(0, -1)$, then draw a line through them.
2. For $y=-3x+4$: Plot points $(\frac{4}{3}, 0)$ and $(0, 4)$, then draw a line through them.
3. The lines intersect at $(\frac{20}{13}, -\frac{8}{13})$ (or approximately $(1.54, -0.62)$).