Question

quick check
y = 2x - 6
y = -4x + 3
(a) graph a
(b) graph b
(c) graph c
(d) graph d

Explanation:

Step1: Find intersection of the two lines

Set $2x - 6 = -4x + 3$
$2x + 4x = 3 + 6$
$6x = 9$
$x = \frac{9}{6} = \frac{3}{2} = 1.5$
Substitute $x=1.5$ into $y=2x-6$:
$y = 2(1.5) - 6 = 3 - 6 = -3$
Intersection point: $(1.5, -3)$

Step2: Identify y-intercepts

For $y=2x-6$, y-intercept is $(0, -6)$
For $y=-4x+3$, y-intercept is $(0, 3)$

Step3: Match to the graph

Check which graph has lines crossing at $(1.5, -3)$, one line crossing y-axis at $(0,-6)$ and the other at $(0,3)$.

Answer:

C. <The graph labeled C with lines intersecting at (1.5, -3), one line with y-intercept (0,-6) and the other with y-intercept (0,3)>