Question

Can someone please help me with this!?

Write an equation for the line in point/slope form and slope/intercept form that has the given condition.

1a. Slope = � and passes through the origin.

1b. Passing through (-2, 4) and (-1, -1).

1c. x-intercept = -5 and y-intercept = -2.


Please and thank you!

Answer 1

first one is \(y=�x\)

Answer 2

2nd one Find the Slope First:

\[m = \frac{ y2-y1 }{ x2-x1 }\]

Answer 3

then use oint Slope Form:

\[y-y1=m(x-x1)\]

Answer 4

1c. Use Intercept Form
:

\[\frac{ x }{ a }+\frac{ y }{ b } = 1\]

Answer 5

a= x intercept

b= y intercept

Answer 6

So these are 3 seperate equations, right?

1A) What's the slope?
--------------------
1B) Use Point-Slope form. y - y1 = m(x - x1)
(-2, 4) and (-1, -1)
Find slope:
\[m = \frac{ y2 - y1 }{ x2 - x1 } = \frac{ (-1) - 4 }{ (-1) - (-2) } = \frac{ (-1) - 4 }{ -1 + 2 }=\frac{ -5 }{ 1 }= -5\]Slope(m) is -5.
So lets use (-2, 4) and the slope (-5) and make an equation in point-slope form.
y - y1 = m(x - x1)
y - 4 = -5(x -(-2))

y - 4 = -5(x + 2)

Get that into Slope-intercept form(y = mx + b), and solve for y.
y - 4 = -5(x + 2)
Distribute.
y - 4 = -5x - 10
Add 4.
y = -5x - 6

SO:
Point-Slope form: y - 4 = -5(x + 2)
Slope-intercept form: y = -5x - 6

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1C)
x-intercept is -5
y-intercept is -2
SO:

So you have 2 points: (-5, 0) and (0, -2)
Find their slope using the same formula as above...
\[m = \frac{ y2 - y1 }{ x2 - x1 } = \frac{ (-2) - 0 }{ 0 - (-5) } = \frac{ (-2) - 0 }{ 0 + 5 }=\frac{ -2 }{ 5 }\]Slope(m) is -2/5
Use point (-5,0) and the slope(-2/5) to make the equation.
y - 0 = -2/5(x - (-5))
y - 0 = -2/5(x + 5)
There is point slope form^

Now slope intercept form.
y - 0 = -2/5(x + 5)
distribute.
y - 0 = -2/5x - 2
add 0.
y = -2/5x - 2

SO:
Point-Slope form: y - 0 = -2/5(x + 5)
Slope-intercept form: y = -2/5x - 2