Consider the line with x-intercept of 2 and y-intercept of -2. What is the equation of this line in standard form?

2 Answers
Feb 20, 2018

y=x-2

Explanation:

An x-intercept of two means we have the point

(2,0)

A y-intercept of negative two means we have the point

(0,-2)

Recall the formula of the slope of a line:

m=(y_2-y_1)/(x_2-x_1)

Since we have two points, we can calculate the slope using ( (x_1,y_1)=(2,0), (x_2,y_2)=(0,-2)

m=(-2-0)/(0-2)

m=1

The point-slope form of a line is:

y-y_1=m(x-x_1)

Where (x_1,y_1) is a point through which the line passes and m is the slope.

We already have m; we can use either of our points for (x_1,y_1), let's use (2,0).

y-0=1(x-2)
y=x-2

Feb 20, 2018

x-y=2

Explanation:

"the equation of a line in "color(blue)"standard form" is.

color(red)(bar(ul(|color(white)(2/2)color(black)(Ax+By=C)color(white)(2/2)|)))

"where A is a positive integer and B, C are integers"

"the equation of a line in "color(blue)"slope-intercept form" is.

•color(white)(x)y=mx+b

"where m is the slope and b the y-intercept"

"to calculate m use the "color(blue)"gradient formula"

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

"let "(x_1,y_1)=(2,0)" and "(x_2,y_2)=(0,-2)

rArrm=(-2-0)/(0-2)=1

rArry=x+blarrcolor(blue)"is the partial equation"

"y-intercept "=(0,-2)rArrb=-2

rArry=x-2larrcolor(red)"in slope-intercept form"

rArrx-y=2larrcolor(red)"in standard form"