Question

Find the slope-intercept form for the equation of the line
which passes through
the point (−1, 3) and has a slope of −2.

y = -2x - 1
y = -2x - 3
y = -2x + 1
y = -2x + 3

Answer 1

First step: find and type in the "point slope form of the equation of a straight line."
Next: Substitute slope value -2 for m in this equation. Substitute the x- and y-coordinates of the given point into this equation. Simplify the result.

Answer 2

is that y-y1=m(x-x1)? @mathmale

Answer 3

so would i put y-3=2(x-(-1))?

Answer 4

That's great. You have been given the value of the slope, m, as well as the coordinates of one point (x, y). Go ahead and substitute all three values into this equation.

Answer 5

Yes! except that the slope, m, is -2, not +2.

Answer 6

Oh right! Sorry. One moment:)

Answer 7

Is it y=-2x+1? @mathmale

Answer 8

Yes. Does this result match any of the answer choices?

Answer 9

Yes!

Answer 10

Thank you very much

Answer 11

Would it be okay if I asked one more question?

Answer 12

sure, please go ahead

Answer 13

Thanks. Ill attach it.

Answer 14

How do I substitute for point of origin?

Answer 15

All four of the answer choices are in slope-intercept form.
"Intercept" most commonly refers to the y-value at which the line crosses the y-axis.
Reading the problem again, what y value do you obtain for the y-intercept / vertical intercept?

Answer 16

2?

Answer 17

First, would you please write out your conception of the "slope-intercept form?"

Answer 18

y=mx+b

Answer 19

Right.

Answer 20

I*f the line passes thru the origin, what is the y-value there?

Answer 21

Hint: what are the coordinates of the origin?

Answer 22

They're (-3,2)

Answer 23

x=-3
y=2

Answer 24

that is the other point. The coord. of the origin are (0,0).

Answer 25

Oh right I see

Answer 26

So, now you have y=mx+b, and know that the line passes thru the origin. b is the y-coordinate of the point at which the line crosses the y-axis. Here, b = ?

Answer 27

So then that means you just have to add the slope into the formula

Answer 28

2

Answer 29

Yes, you'll need to calculate the slope and insert your result into the formula.

Answer 30

What happened to the 3?

Answer 31

0

Answer 32

Wait, sorry

Answer 33

The line passes thru (-3,2) as well as thru (0,0).

Answer 34

Would this line have a pos. or a neg. slope, and how would you know that?

Answer 35

negative? because the 3 is negative?

Answer 36

Sorry im new at this and just a bit confused

Answer 37

I'd prefer you actually see the line involved here. It goes thru (-3,2) and (0,0).

Answer 38

so then would it be -3/2x?

Answer 39

does the function seem to be increasing or decreasing as x increases?

Answer 40

Decreasing

Answer 41

Slope = rise / run.

Here, the change in y as you progress from (-3,2) to (0,0) is -2 and the change in x is 3.

So, your slope is rise / run = -2/3

Answer 42

Slope does not involve x here; the slope is a constant coefficient in front of the "x". x is your independent variable.

Answer 43

Okay

Answer 44

So, in this case, the slope is... ?
and the y-intercept, b, is ... ?

and the correct choice of answer is ... ?

Answer 45

So if it's rise over run -2/3, would y=-2/3x?

Answer 46

If the y-intercept is 0

Answer 47

Yes, if " b " equals zero, then the entire equation of the line boils down to y=(-2/3) x.

Answer 48

Okay, I definitely understand better now. Thank you very much.

Answer 49

I'm so glad to have been of help. Good luck to you!