Question

line a
y - intercept
slope
equation
line b
y - intercept
slope
equation $y = x + 4$

Explanation:

Step1: Identify Line B's values

Line B equation is given as $y = x + 4$. Using slope-intercept form $y=mx+b$ (where $m$=slope, $b$=y-intercept):

• y-intercept: $4$
• Slope: $1$

Step2: Find Line A's y-intercept

Line A crosses the y-axis at $(0, 4)$? No, observe the vertical line intersection: Line A passes through $(0, -6)$? Wait, no, use intersection points. Line A and B intersect at $(-4, 0)$. Line A also passes through $(0, -6)$? No, wait, Line A goes through $(0, -6)$? No, let's use two points on Line A: $(0, -6)$ and $(-4, 0)$.
Y-intercept is the y-value when $x=0$: $-6$

Step3: Calculate Line A's slope

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$. Use points $(-4, 0)$ and $(0, -6)$:
$m=\frac{-6-0}{0-(-4)}=\frac{-6}{4}=-\frac{3}{2}$? No, wait, no—wait Line A goes down from left to right. Wait, no, the vertical line: Line A passes through $(0, -6)$ and $(-4, 0)$? No, wait the intersection point is $(-4, 0)$. Line B is $y=x+4$, so when $x=0$, $y=4$ (Line B's y-intercept is (0,4)). Line A: when $x=0$, $y=-6$ (y-intercept), and when $x=-4$, $y=0$. So slope is $\frac{0-(-6)}{-4-0}=\frac{6}{-4}=-\frac{3}{2}$? No, wait no, let's check the grid: each square is 1 unit. Line A goes from $(0, -6)$ up 3, left 2 to $(-2, -3)$, then up 3 left 2 to $(-4, 0)$. Yes, slope is $\frac{\Delta y}{\Delta x}=-\frac{3}{2}$.

Step4: Write Line A's equation

Using $y=mx+b$, $m=-\frac{3}{2}$, $b=-6$:
$y=-\frac{3}{2}x -6$

Wait, no, wait the intersection point: Line B is $y=x+4$, at $x=-4$, $y=0$, which matches. Line A at $x=-4$, $y=0$: $0=-\frac{3}{2}(-4)-6=6-6=0$, correct.

Wait, alternatively, maybe Line A passes through $(0, 4)$? No, Line B passes through $(0,4)$. Line A passes through $(0, -6)$ and $(-4, 0)$. Yes, that's correct.

Answer:

LINE A

y-intercept: $\boldsymbol{-6}$
Slope: $\boldsymbol{-\frac{3}{2}}$
Equation: $\boldsymbol{y=-\frac{3}{2}x -6}$

Line B

y-intercept: $\boldsymbol{4}$
Slope: $\boldsymbol{1}$
Equation: $\boldsymbol{y=x+4}$