#### Question

# Explain how to find the equation of the line, in standard form and slope–intercept f?

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

Required equation is

y+7=( -1+7)/(1+1)*(x+1)

y+7=3(x+1)

y+7= 3x+3

3x-y-4=0

y=3x-4

Part 2

In slope intercept form we soon find its slope and the point at which the line intersects the y-axis

Slope-intercept form: y = mx + b

Standard form: Ax + By = C

http://en.wikipedia.org/wiki/Linear_equa…

slope = (-7+1)/(-1-1) = -6/-2 = 3

Since we have one point (1, -1) and the slope (3), we will start with yet another form: point-slope form and then rewrite in slope-intercept form

y + 1 = 3 (x - 1)

y = 3x - 3 - 1

y = 3x - 4

Standard form:

3x - y = 4

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In slope-intercept form, you can very easily determine:

slope = m = 3 and

y-intercept = b = -4

In standard form, you can determine somewhat easily:

x-intercept = C/A = 4/3

y-intercept = C/B = 4/-1 = -4

1. First obtain the slope,m of the line giving by m=(y2-y1)/(x2-x1), where, x1=-1, y1=-7, x2=1 and y2=-1, thus,

m=(-1+7)/(1+1)=6/2=3.

The equation of the line is

y-y2=m(x-x2), thus,

y+1=3(x-1)=3x-3, whence,

3x-y-4=0 is the equation of the line in standard form. The slope-intercept form can be obtained by putting the equation in the form y=mx+c, thus from the equation in standard form above, y=3x-4, where slope, m=3 and intercept, c=-4.

2. The slope-intercept readily gives the slope of the line as indicated by the coefficient of x and the point at which the line cuts the y-axis, the standard form does not give at a glance, slope and intercrpts, in the standard form, one can easily obtain the perpendicular distance of a point from a line.the equation in standard form above, y=3x-4, where slope, m=3 and intercept, c=-4.

2. The slope-intercept readily gives the slope of the line as indicated by the coefficient of x and the point at which the line cuts the y-axis, the standard form does not give at a glance, slope and intercrpts, in the standard form, one can easily obtain the perpendicular distance of a point from a line.