Question

A line has an x-intercept of 8 and a y-intercept of 3. What is the equation of the line?

Answer 1

y = (-3/8)x + 3

Multiply through by 8

8y = -3x + 24

Step-by-step explanation

The slope and y-intercept form of the equation of a straight line is given as

y = mx + b

where

y = y-coordinate of a point on the line.

m = slope of the line.

x = x-coordinate of the point on the line whose y-coordinate is y.

b = y-intercept of the line.

So, we just need to solve for the slope of this line.

For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as

`Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=(y_2-y_1)/(x_2-x_1)`

For this question, the x and y intercepts are given. Since these are points where the line crosses the x and y axis, we can write them in coordinates form as

x-intercept = (8, 0)

y-intercept = (0, 3)

(x₁, y₁) and (x₂, y₂) are (8, 0) and (0, 3)

`\text{Slope = }(3-0)/(0-8)=(3)/(-8)=-(3)/(8)`

y = mx + b

m = slope = -(3/8)

b = y-intercept = 3

y = mx + b

y = (-3/8)x + 3

Multiply through by 8

8y = -3x + 24

Hope this Helps!!!