Answer
(a) slope = $2.5$
(b) Refer to the graph below.
Work Step by Step
Solve for $y$:
$5x-2y=10
\\5x-2y-5x=10-5x
\\-2y=-5x+10
\\\frac{-2y}{-2}=\frac{-5x+10}{-2}
\\y=\frac{-5x}{-2} + \frac{10}{-2}
\\y=2.5x - 5$
This means the given equation is equivalent to $y=2.5x-5$.
RECALL:
In the linear equation $y=mx + b$, $m$=slope and $(0, b)$ is the y-intercept.
(a) The line $y=2.5x-5$ has a slope of $2.5$ and a y-intercept of $(0, -5)$.
(b) To graph the line, perform the following steps:
(1) Plot the y-intercept $(0, -5)$.
(2) Use the slope to plot another point.
The slope is $2.5$ so there is a 2.5-unit decrease in the value of $y$ for every 1-unit increase in $x$. From $(0, -5)$, move 2.5 units up (the rise) and 1 unit to the right (the run) to reach $(1, -2.5)$. Plot $(1, -2.5)$.
(3) Complete the graph by connecting the two points using a line.
(Refer to the graph in the answer part above.)