Question

10.
equation =
11.
equation =

1. 5x + 15y = 30

equation =

1. -6x + 4y = 20

equation =
write the equation of the line in slope - intercept form.

Explanation:

Step1: Problem 10: Identify line features

The vertical line passes through $x=2$. Slope-intercept form for vertical lines is $x=a$, but since slope-intercept $y=mx+b$ can't represent vertical lines, we state it as $x=2$ (note: vertical lines have undefined slope, no y-intercept).

Step2: Problem 11: Calculate slope

Pick points $(0,1)$ and $(4,2)$. Slope $m=\frac{2-1}{4-0}=\frac{1}{4}$.

Step3: Problem 11: Identify y-intercept

The line crosses y-axis at $(0,1)$, so $b=1$.

Step4: Problem 11: Write slope-intercept form

Substitute $m=\frac{1}{4}$ and $b=1$ into $y=mx+b$.
$y=\frac{1}{4}x+1$

Step5: Problem 12: Isolate $15y$

Subtract $5x$ from both sides.
$15y = -5x + 30$

Step6: Problem 12: Solve for $y$

Divide all terms by 15.
$y = \frac{-5x}{15} + \frac{30}{15}$
Simplify: $y=-\frac{1}{3}x+2$

Step7: Problem 13: Isolate $4y$

Add $6x$ to both sides.
$4y = 6x + 20$

Step8: Problem 13: Solve for $y$

Divide all terms by 4.
$y = \frac{6x}{4} + \frac{20}{4}$
Simplify: $y=\frac{3}{2}x+5$

Answer:

1. Equation = $x=2$
2. Equation = $y=\frac{1}{4}x+1$
3. Equation = $y=-\frac{1}{3}x+2$
4. Equation = $y=\frac{3}{2}x+5$