Question

graph the system of equations.$y=\frac{4}{5}x+1$$y=-\frac{1}{5}x+6$

Explanation:

Step1: Identify slope-intercept form

Both equations use $y=mx+b$, where $m$=slope, $b$=y-intercept.

Step2: Analyze $y=\frac{4}{5}x+1$

• Y-intercept: $b=1$, so plot $(0,1)$.
• Slope: $m=\frac{4}{5}$, so from $(0,1)$, move 5 right, 4 up to $(5,5)$. Draw the line through these points.

Step3: Analyze $y=-\frac{1}{5}x+6$

• Y-intercept: $b=6$, so plot $(0,6)$.
• Slope: $m=-\frac{1}{5}$, so from $(0,6)$, move 5 right, 1 down to $(5,5)$. Draw the line through these points.

Step4: Verify intersection

Solve $\frac{4}{5}x+1 = -\frac{1}{5}x+6$:
$$\frac{4}{5}x+\frac{1}{5}x=6-1$$
$$x=5$$
Substitute $x=5$: $y=\frac{4}{5}(5)+1=5$. Intersection at $(5,5)$.

Step5: Match to correct graph

The lower graph has lines intersecting at $(5,5)$, matching the equations' intercepts and slope.

Answer:

The correct graph is the lower one (the second grid with lines intersecting at (5, 3) is incorrect; the valid graph has $y=\frac{4}{5}x+1$ crossing the y-axis at (0,1) and $y=-\frac{1}{5}x+6$ crossing the y-axis at (0,6), intersecting at (5,5)).