Question

Find an equation of the line that has intercepts (1,0) and (0,4).

a) y = -4x + 1
b) y = 4x + 1
c) y = -4x - 1
d) y = 4x - 1

Answer 1

To find the equation of a line with intercepts
`(1,0) and (0,4)`, we can use the slope-intercept form of a linear equation. The equation of the line is
`y = -4x + 4.`

Step-by-step explanation:

To find the equation of a line with intercepts
`(1,0) and (0,4)`, we can use the slope-intercept form of a linear equation, which is
`y = mx + b`,

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

First, let's find the slope using the formula
`(y2 - y1) / (x2 - x1)`.

The two intercepts are
`(1,0) and (0,4)`, so the slope is

`(0 - 4) / (1 - 0) = -4 / 1 = -4`.

Next, we can substitute the slope and one of the intercepts into the equation
`y = mx + b`.

Let's use the point
`(1,0): 0 = -4(1) + b`. Solving for b, we get
`b = 4`.

Therefore, the equation of the line with intercepts
`(1,0) and (0,4)` is

`y = -4x + 4`.