(A) Find the slope of the line that passes through the given points.

1 answer:

6 0

$(\stackrel{x_1}{-3}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{(-3)}}} \implies \cfrac{0}{6 +3}\implies 0$

hmmm a line with a slope of 0 is a horizontal one, and it has no slope-intercept form.

Check the picture below.

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Step-by-step explanation:

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Graph the function -2x+5y=10

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An equation of the form ax+by+c=0, where x, y are variable, and a, b, c are numbers, is called a "linear equation"

the reason we call it linear, is that all solutions (x, y) to this equation, when plotted in the x-y axis, form a line.

To draw this line, 2 points are enough, that is 2 solutions (x, y) of the equation.

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-2x+5y-10=0 is a linear equation (a=-2, b=5, c=-10)

to find 2 solutions, we set x or y any value we want, and solve for the other

for example:

let x=0,

then

-2x+5y-10=0 becomes 5y-10=0, so y=2

this gives us the solution (0, 2)

another example; set y=0

then -2x+5y-10=0 becomes -2x-10=0; -2x=10 so x=-5

thus another solution is (-5, 0)

Draw these 2 points, and join them with a line, as shown in the figure.