Question

Complete the equation for the standard form of the line that has an x-intercept of –4 and a y-intercept of 3

Answer 1

The equation for the standard form of the line will be:

• 3x + (-4y) = -12

Explanation:

Given

• x-intercept = –4

• y-intercept = 3

The equation of a line in standard form

• Ax + By = C

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

We know the equation of a line in slope-intercept form

y = mx+b

where m is the slope and b the y-intercept

To calculate the slope, use the gradient formula

m = y₂-y₁ / x₂-x₁

let

(x₁, y₁) = (-4, 0) ∵ x-intercept = (-4, 0)

(x₂, y₂) = (0, 3) ∵ y-intercept = (0, 3)

m = y₂-y₁ / x₂-x₁

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

= 3 / 4

Thus, the equation in slope-intercept form:

y = mx+b

y = 3/4x + 3

• Writing in standard form

Multiply y = 3/4x + 3 by 4

4y = 3x + 12

3x-4y = -12

3x + (-4y) = -12

Thus, the equation for the standard form of the line will be:

• 3x + (-4y) = -12