Can someone please explain how I do the following problem?

Question

"Write the point-slope form of the equation of the line described"

23. through: (-2, 4), parallel to y= -5/2(x) + 5

Answer 1

The Slope-Intercept Form of an equation is    Y  =  M * X  +  B, where M is the slope and B is the [Y-axis] intercept.

 

The Point-Slope Form of an equation is   (Y - y)  =  M * (X - x), where M is the slope, "y" is the y-value of the point, and "x" is the x-value of the point.

 

The Standard Form of an equation is   A*X   +/-   B*Y  =  C    ( or A*X + B*Y + C = 0 ), where A, B and C are integer values.

This was used when scientific treatises were written in Latin. Latin, or Roman numerals, do not allow for decimal numbers. Also, think about the problem of expressing a fraction in Roman numerals yeecch!

 

Now, what do parallel lines have in common?

Answer 2

Hi Dylan,

 

Point-slope form of an equation for a line is the easiest way to find a line's equation when you know only a) one point on that line, and b) its slope.  Point-slope form is expressed as follows, where y₁ = the y coordinate for the point you know, and x₁ = the x-coordinate for the same point:

 

y - y₁ = m(x - x₁)

 

y, x, and m are the variables for ANY y-coordinate on the line, any x coordinate on the line, and the slope of the line, respectively.  You might recognize these from the more familiar slope-intercept formula of y = mx + b.

 

Ok, so on to this line:

 

For a), our point is given:  ( - 2, 4).  So we plug these into the point-slope equation:

 

y - 4 = m(x - [-2])

 

We can simplify a little:

 

y - 4 = m(x + 2)

 

But what is the slope?  You probably know it's impossible to determine slope from just one point (since a literal infinity of possible lines through it!), so... ah-ha!  This is where b) comes in:  if the line y = -5/2(x) + 5 is PARALLEL to our line, then our line will have the same slope:  -5/2.  This is because any lines that are parallel to each other necessarily have the same slope.

 

So now, we're done:

 

y - 4 = -5/2(x + 2)

 

That's the line in point-slope equation form.  If you wanted (or more likely, were required!) to change that into slope-intercept form, you would use basic algebra:

 

y - 4 = -5/2x + (-5/2)(2/1)

y - 4 = -5/2x + (-5)

y - 4 = -5/2x - 5

y = -5/2x - 1

 

I hope this helps!

 

Evan

 

Answer 3

Two lines are parallel if their slopes are equal so the line we are looking for has a slope of -5/2 and must satisfy the following relation y-4=(-5/2)(x+2) this is the "point slope from"

 

so y=(-5/2)x-1 is the equation.

 

Hope this helps

 

Jim