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Elina [12.6K]
2 years ago
14

Consider the graph below: What is the equation of the line in slope-intercept form?

Mathematics
1 answer:
lora16 [44]2 years ago
5 0

Answer:

y=\frac{-5}{4}x+5

Step-by-step explanation:

Slope intercept form: y=mx+b where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)

<u>1) Find the slope of the line (</u>m<u>)</u>

To do this, we can plug the two given points (0,5) and (4,0) into the slope equation:

\frac{y_2-y_1}{x_2-x_1} \\= \frac{0-5}{4-0}\\= \frac{-5}{4}

Therefore, the slope of the line is \frac{-5}{4}.

<u>2) Find the y-intercept of the line (</u>b<u>)</u>

Recall that the y-intercept is the value of y when the line crosses the y-axis. We don't actually need to perform any calculations because on the graph, we can see that the line crosses the y-axis when y=5.

Therefore, the y-intercept of the line is 5.

Plugging both m and b into y=mx+b, we have a final equation of:

y=\frac{-5}{4}x+5

I hope this helps!

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Answer:

Required solution (a) f(x,y,z)=xyz+3z^2+C (b) 40.

Step-by-step explanation:

Given,

F(x,y,z)=yz \uvec i +xz\uvec j+(xy+6z)\uvex k

(a) Let,

F(x,y,z)=yz \uvec i +xz\uvec j+(xy+6z)\uvex k=f_x \uvec{i} +f_y \uvex{j}+f_z\uvec{k}

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f_y=xz+g'(y,z)

compairinfg with f_y=xz of the given function we get,

g'(y,z)=0\implies g(y,z)=0+h(z)\implies g(y,z)=h(z)

Then,

f(x,y,z)=xyz+h(z)

Again differentiate with respect to z we get,

f_z=xy+h'(z)=xy+6z

on compairing we get,

h'(z)=6z\implies h(z)=3z^2+C   (By integrating h'(z))  where C is integration constant. Hence,

f(x,y,z)=xyz+3z^2+C

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