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Write an equation of the line given an intercepts. Express in standard form.

1. x – intercept is 4 and y – intercept is 3.
2. x – intercept is -2 and y – intercept is 5.

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Answer:

Required equations in standard form are:

1. 3x+4y=12

2. -5x+2y = 10

Explanation:

Standard form of equation is given as:


Ax+By = C

1. x – intercept is 4 and y – intercept is 3.

The points will be:

(4,0) and (0,3)

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


m = (3-0)/(0-4)\\m = -(3)/(4)

Slope intercept form of line is:


y = mx+b

Putting the values of m and b(y-intercept)


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

Multiplying whole equation by 4


4y = -3x+12\\3x+4y = 12

2. x – intercept is -2 and y – intercept is 5

The points will be:

(-2,0) and (0,5)

Now


m = (5-0)/(0+2)\\m = (5)/(2)

Putting the values of m and b in slope intercept form


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

Multiplying the equation by 2


2y = 5x+10


-5x+2y=10

Hence,

Required equations in standard form are:

1. 3x+4y=12

2. -5x+2y = 10

User Bendewey
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