Question

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

Answer 1

Answer:

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:

$\text{Slope(m)} = \frac{y_2-y_1}{x_2-x_1}$

then;

$m = \frac{2-(-4)}{6-(-3)}=\frac{6}{9} = \frac{2}{3}$

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

$y-(-4) = \frac{2}{3}(x-(-3))$

⇒$y+4 = \frac{2}{3}(x+3)$

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

x-intercept:

Substitute y =0 and solve for x:

then;

$0+4 = \frac{2}{3}(x+3)$

⇒$4 = \frac{2}{3}(x+3)$

⇒$2 = \frac{1}{3}(x+3)$

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

Answer 2

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