Question

$y = 4x - 7$
$y = x - 1$
which of the following is the graph of the given system of equations?
choose 1 answer:

Explanation:

Step1: Identify slopes and y-intercepts

For $y=4x-7$: slope $m_1=4$, y-intercept $b_1=-7$.
For $y=x-1$: slope $m_2=1$, y-intercept $b_2=-1$.

Step2: Find intersection point

Set $4x-7=x-1$
$4x-x=-1+7$
$3x=6$
$x=2$
Substitute $x=2$ into $y=x-1$: $y=2-1=1$.
Intersection: $(2,1)$.

Step3: Match to graph

Both lines have positive slopes, cross at $(2,1)$, with $y=4x-7$ steeper and lower y-intercept.

Answer:

C. <The graph showing two positively sloped lines intersecting at (2,1), with the steeper line crossing the y-axis below the other>