Question

Find the equation of a line that passes through the points (-4, -2) and (6, 3).

Answer 1

Answer:

$y=\frac{1}{2} x$

Step-by-step explanation:

The equation of a line through two points can usually (except when the line is a vertical line) be written in slope intercept form,  $y=mx+b$ , where "m" is the slope of the line, and "b" is the y-intercept of the line.

General outline

1. Find the slope
2. Find the y-intercept

Step 1.  Find the slope

To find "m", use the formula for slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

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

$m=\dfrac{3+2}{6+4}$

$m=\dfrac{5}{10}$

$m=\dfrac{1}{2}$

So, the slope is 1/2 and we know that the equation for the line that passes through these two points should look like: $y=\frac{1}{2} x+b$

Step 2.  Find the y-intercept

To find "b", substitute one of the known points, and solve for "b":

$y=\frac{1}{2} x+b$

$(3)=\frac{1}{2} (6)+b$

$3=3+b$

Subtracting 3 from both sides to isolate the "b"...

$(3)-3=(3+b)-3$

$0=b$

So, the y-intercept is 0.  Substituting into our line equation, $y=\frac{1}{2} x+(0)$ which simplifies to $y=\frac{1}{2} x$