Algebra Help Please??

Question

Write the point-slope form of the equation of the line that passes through the point and has the given slope. Then rewrite the equation in slope-intercept form.

-- (0, 8) , m = 1/4

-- (-1, -7) , m = 4


Write an equatoin in standard form of the line that passes through the given point and has the given slope, or that passes through the two points.

-- (-1, 0) , (-5 , -3)

Hey Ya'll! I could really use some help on these...I was absent for a while and I ned to get caught up on this and I need to understand it...lol...and my teacher doesn't teach very well so yea...Thanks in advanced!! lol
Ciao for now,
Tara

Answer 1

The point-slope form on its own is written as:

y - y1 = m(x - x1)

Here the values for x1 and y1 are replaced with those from the coordinate given to you, and the slope value is substituted for m. The entire equation is just rearranged algebraically to solve for y and get it into slope-intercept form: y = mx + b.

y - 8 = 1/4(x - 0)
y - 8 - 1/4x
y = 1/4x + 8

y - (-7) = 4(x - (-1))
y + 7 = 4(x + 1)
y + 7 = 4x + 4
y = 4x -3

For the third problem, the main difference is that you have the extra step of solving for the slope yourself, which you can do by taking the chance in the y values and dividing them by the change in the x values.

(-3 - 0)/(-5 -(-1))
(-3)/(-5 + 1)
-3/-4
3/4 = m = slope

You can then plug this value for m along with the x and y values from either coordinate into the point-slope form of the equation. Either point will work:

y - 0 = 3/4(x - (-1))
y = 3/4(x + 1)
y = 3/4x + 3/4

Hope that helps!

Answer 2

1) 2)
Point- slope: y-8= 1/4( x - 0 ) Point-slope: y+7= 4 ( x + 1 )

Slope- intercept: y= 1/4x + 8 Slope-intercept: y= 4x -3

3) slope: 3/4

Answer 3

I will do the first two. y-8=1/4(x-0) so y=1/4x+8
Now for the second: y+7=4(x+1) so y+7=4x+4 so y=4x-3