Question

1. $y = x - 4$
2. $y = -\frac{4}{5}x$

for problems 6-8, write the equation of the line in slope-intercept form.
6.
7.

Explanation:

Problem 4: Graph $y=x-4$

Step1: Identify intercepts

x-intercept: set $y=0$, $0=x-4 \implies x=4$; point $(4,0)$
y-intercept: set $x=0$, $y=0-4=-4$; point $(0,-4)$

Step2: Plot and draw line

Mark $(4,0)$ and $(0,-4)$, connect with straight line.

Problem 5: Graph $y=-\frac{4}{5}x$

Step1: Identify key points

y-intercept: set $x=0$, $y=0$; point $(0,0)$
Another point: set $x=5$, $y=-\frac{4}{5}(5)=-4$; point $(5,-4)$

Step2: Plot and draw line

Mark $(0,0)$ and $(5,-4)$, connect with straight line.

Problem 6: Find slope-intercept form

Step1: Identify intercepts

x-intercept: $(9,0)$; y-intercept: $(0,7)$

Step2: Calculate slope

$m=\frac{0-7}{9-0}=-\frac{7}{9}$

Step3: Write equation

Use $y=mx+b$, $b=7$: $y=-\frac{7}{9}x+7$

Problem 7: Find slope-intercept form

Step1: Identify two points

Points $(1,0)$ and $(2,9)$

Step2: Calculate slope

$m=\frac{9-0}{2-1}=9$

Step3: Find y-intercept

Substitute $(1,0)$ into $y=9x+b$: $0=9(1)+b \implies b=-9$

Step4: Write equation

$y=9x-9$

Answer:

1. For $y=x-4$: Graph passes through $(4,0)$ and $(0,-4)$, straight line connecting these points.
2. For $y=-\frac{4}{5}x$: Graph passes through $(0,0)$ and $(5,-4)$, straight line connecting these points.
3. Problem 6: $y=-\frac{7}{9}x+7$
4. Problem 7: $y=9x-9$