Question

Use the given conditions to write an equation for the line in point-slope form. Passing through (2,-3) with x-intercept = -2

Answer 1

The equation for line is
`y=-(3)/(4) x-(3)/(2)`

Step-by-step explanation:

It is given that the line passes through the point
`(2,-3)` with x-intercept = -2

The x intercept is the value of x when y = 0.

Thus, it can be written in coordinate as
`(-2,0)`

Now, we shall determine the slope using the points
`(2,-3)` and
`(-2,0)`

`m=(y_2-y_1)/(x_2-x_1)`

Substituting, we get,

`m=(0+3)/(-2-2) \\m=-(3)/(4)`

Thus, the slope is
`m=-(3)/(4)`

Now, we shall substitute the point
`(2,-3)` and slope
`m=-(3)/(4)` in the point-slope formula
`y-y_1=m(x-x_1)`, we get,

`y+3=-(3)/(4) (x-2)`

Multiplying both sides by 4, we get,

`4y+12=-3x+6`

Subtracting both sides by 12,

`4y=-3x-6`

Dividing both sides by 4, we get,

`y=-(3)/(4) x-(3)/(2)`

Thus, the equation of the line is
`y=-(3)/(4) x-(3)/(2)`