Question

y = 4x - 7
y = x - 1
which of the following is the graph of the given system of equations?
choose 1 answer:
a (graph with two lines intersecting, one with negative slope, one steeper negative slope)
b (graph with two lines intersecting, one with negative slope, one steeper negative slope)
c (graph with two lines intersecting, one with positive slope, one steeper positive slope)
d (graph with two lines intersecting, one with positive slope, one steeper positive slope)

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, steeper line is $y=4x-7$, intersect at $(2,1)$.

Answer:

C. <The graph with two positively sloped lines, steeper line crossing y-axis at -7, shallower line crossing y-axis at -1, intersecting at (2,1)>