Question

Part 1: Using complete sentences, explain how to find the equation of the line, in standard form and slope–intercept form, passing through (–1, –7) and (1, –1). (4 points)

Part 2: Compare the benefits of writing an equation in standard form to the benefits of writing an equation in slope–intercept form. (3 points)

Answer 1

first you need to find the slope by using the slope formula :
slope(m) = (y2 - y1) / (x2 - x1)
(-1,-7) x1 = -1 and y1 = -7
(1,-1) x2 = 1 and y2 = -1
now we sub
slope(m) = (-1 - 7) / (1 - (-1)
slope(m) = -8/(1 + 1)
slope(m) = -8/2 reduces to - 4
so our slope is -4.

Now we will use point slope form, y - y1 = m(x - x1), using slope = -4 and either of your set of points.
I will use (1,-1)....x1 = 1 and y1 = -1
now we sub
y - y1 = m(x - x1)
y - (-1) = -4(x - 1)
y + 1 = -4(x - 1) ====> this is point slope form

y + 1 = -4(x - 1) -- distribute through the parenthesis
y + 1 = -4x + 4 -- subtract 1 from both sides
y = -4x + 4 - 1
y = -4x + 3 ===> this is slope intercept form

y = -4x + 3 -- add 4x to both sides
4x + y = 3 ===> this is standard form

Answer 2

any questions ?