Question

(1 point)
for the lines defined by the following equations indicate with a \v\ if they are vertical, an \h\ if they are horizontal, and an \s\ (for slanted) if they are neither vertical nor horizontal.
$3x + 4y+5 = 0$
$4y + 5 = 0$
$3x + 5 = 0$
$x = 1$
$y = 1$
$y = x$
hint: draw the graphs of these lines.

Explanation:

Step1: Analyze $3x + 4y+5 = 0$

Rewrite in slope - intercept form $y=mx + b$. Solving for $y$ gives $y=-\frac{3}{4}x-\frac{5}{4}$. Since it has a non - zero slope $m =-\frac{3}{4}$, it is slanted.

Step2: Analyze $4y + 5 = 0$

Solve for $y$: $y=-\frac{5}{4}$. It is a horizontal line as it is of the form $y = k$ (constant).

Step3: Analyze $3x+5 = 0$

Solve for $x$: $x =-\frac{5}{3}$. It is a vertical line as it is of the form $x = k$ (constant).

Step4: Analyze $x = 1$

It is of the form $x = k$ (constant), so it is a vertical line.

Step5: Analyze $y = 1$

It is of the form $y = k$ (constant), so it is a horizontal line.

Step6: Analyze $y=x$

It has a slope $m = 1$. Since it has a non - zero slope, it is slanted.

Answer:

$3x + 4y+5 = 0$: S
$4y + 5 = 0$: H
$3x+5 = 0$: V
$x = 1$: V
$y = 1$: H
$y=x$: S