Question

sketch the graph of each line.
$8x - 5y = -25$
a)
image of a graph
b)
image of a graph
c)
image of a graph
d)
image of a graph

Explanation:

Step1: Convert to slope-intercept form

Isolate $y$ from $8x - 5y = -25$:

$$\begin{align*} -5y &= -8x -25\\ y &= \frac{8}{5}x + 5 \end{align*}$$

Step2: Identify y-intercept

The y-intercept is $b=5$, so the line crosses the y-axis at $(0, 5)$.

Step3: Identify x-intercept

Set $y=0$ and solve for $x$:

$$\begin{align*} 0 &= \frac{8}{5}x + 5\\ \frac{8}{5}x &= -5\\ x &= -\frac{25}{8} = -3.125 \end{align*}$$

So the line crosses the x-axis at $(-3.125, 0)$.

Step4: Match to the graph

The line with y-intercept $(0,5)$ and x-intercept near $(-3,0)$ is option A.

Answer:

A) <Graph with line crossing y-axis at (0,6) and x-axis near (-3,0)>