Find the slope of the line.

Mathematics

1 answer:

ElenaW [278]2 years ago

5 0

Answer:

$-\frac{5}{4}$

Step-by-step explanation:

$m=\frac{rise}{run}=\frac{-4-1}{1+3}=\frac{-5}{4} =-\frac{5}{4}$

Hope this helps.

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In each part that follows, you are given an equation of a line and a point. Find the equation of the line through the given poi

Semmy [17]

Answer:

a) $y=-\frac{1}{9}x$

b) $y-2=-\frac{1}{3} (x-1)$

Step-by-step explanation:

We can write the equation of a line in 3 different forms including slope intercept, point-slope, and standard depending on the information we have. We have a point given and a slope from the equation. We will chose point-slope since we have a point and can find the slope.

Point slope: $y-y_1=m(x-x_1)$

a) $m\neq 9$ in our new equation because it is perpendicular to it. This means we will need to change it into its negative reciprocal which is $m=-\frac{1}{9}$ .

We will substitute $m=-\frac{1}{9}$ and $x_1=0\\y_1=0$ .

$y-0=-\frac{1}{9} (x-0)$

This simplifies to:

$y=-\frac{1}{9}x$

b) The equation y=3x+4 follows y=mx+b. For the perpendicular line, $m\neq 3$ . We will need to change it into its negative reciprocal which is $m=-\frac{1}{3}$ .