Question

A line passes through the points (–3, –4) and (6, 2).What is the x-intercept of this line?

Answer 1

your x-intercept is 3 and I don't know why I have to do 20 characters for an answer that involves 3 words and 1 number

Answer 2

Point-Slope form:

The equation of line is given by:

`y-y_1 = m(x-x_1)`

where,

m is the slope of the line and
`(x_1, y_1)` is the point on the line.

As per the statement:

A line passes through the points (–3, –4) and (6, 2).

Using slope formula:

`\text{Slope(m)} = (y_2-y_1)/(x_2-x_1)`

then;

`m = (2-(-4))/(6-(-3))=(6)/(9) = (2)/(3)`

Substitute the given values and m = 2/3 we have;

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

⇒
`y+4 = (2)/(3)(x+3)`

We have to find the x-intercept of this line.

x-intercept:

Substitute y =0 and solve for x:

then;

`0+4 = (2)/(3)(x+3)`

⇒
`4 = (2)/(3)(x+3)`

⇒
`2 = (1)/(3)(x+3)`

Multiply both sides by 3 we have;

`6 = x+3`

Subtract 3 from both sides we have;

3 = x

or

x = 3

therefore, the x-intercept of this line is, 3