Question

Find an equation for the line with the given properties.

x-intercept = 2; y-intercept = -3. y =

Answer 1

`y=\displaystyle(3)/(2)x-3`

Explanation:

Hi there!

Slope-intercept form:
`y=mx+b` where m is the slope and b is the y-intercept (the value of y when x=0)

We're given:

⇒ x-intercept = 2

⇒ y-intercept = -3

1) Determine the slope (m)

`m=\displaystyle(y_2-y_1)/(x_2-x_1)` where two points that fall on the line are
`(x_1,y_1)` and
`(x_2,y_2)`

Given the x- and y-intercepts, we can rewrite them as points:

x-intercept = 2

⇒ (2,0)

y-intercept = -3

⇒ (0,-3)

Plug these points into the equation:

`m=\displaystyle(0-(-3))/(2-0)\\\\m=\displaystyle(0+3)/(2)\\\\m=\displaystyle(3)/(2)`

Therefore, the slope of the line is
`\displaystyle(3)/(2)`. Plug this into
`y=mx+b`:

`y=\displaystyle(3)/(2)x+b`

2) Plug in the y-intercept (b)

`y=\displaystyle(3)/(2)x+b`

We're given the y-intercept: -3. Plug this into
`y=\displaystyle(3)/(2)x+b`:

`y=\displaystyle(3)/(2)x+(-3)\\\\y=\displaystyle(3)/(2)x-3`

I hope this helps!