Question

Give the points (4,2) and (-4,6). What is the equation of the line in slope intercept form?

Answer 1

Slope-intercept form: y = mx + b  (m is the slope, b is the y-intercept or the y value when x = 0  --->  (0, y))

To find the slope(m), you use the slope formula:

$m=\frac{y_2-y_1}{x_2-x_1}$  And plug in the two points

(x₁ , y₁) = (4, 2)

(x₂ , y₂) = (-4, 6)

$m=\frac{6-2}{-4-4}$

$m=\frac{4}{-8}$

$m=-\frac{1}{2}$

$y=-\frac{1}{2}x+b$   To find b, plug in either of the two points into the equation

(4, 2)

$2 = -\frac{1}{2}(4)+b$

2 = -2 + b   Add 2 on both sides to get b by itself

4 = b

$y = -\frac{1}{2}x+4$