Question

Write an equation in slope - intercept form for the line that passes through the given paint andis parallel to the given equation.4.(-4, 2), y = -1/2x+ 6

Answer 1

When two equation are parallel it means they have the same slope.

You have the equation:

`y=-(1)/(2)x+6`

You can identify the slope(m) as the number next to the x in equation that follow the next form:

`y=mx+b`

Then, the equation parallel to the given equation has an slope of:

m= - 1/2

Now, if we have a point of the equation we can find the value of the b (y-intercept) in the slope - intercept form of a lineal equation:

`y=mx+b`

The given point is ( -4 , 2)

You have the next values:

m= - 1/2

y= 2

x= -4

Then we substitute that values:

`2=-(1)/(2)(-4)+b`

And clear the b:

`2=(4)/(2)+b`
`2=2+b`
`2-2=2-2+b`
`0=b`

Now, we get the value of the slope (m= - 1/2) and the y-intercept (b=0)

We can write the equation in slope - intercept form:

`y=-(1)/(2)x+0`

or:

`y=-(1)/(2)x`