Question

What is the equation of the line passing through the pair of points. Write the equation in slope-intercept form. (9,5) and (5,9)

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) or the point where the line crosses through the y-axis)

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

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

(5, 9) = (x₁, y₁)

(9, 5) = (x₂, y₂)

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

$m=\frac{5-9}{9-5}$

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

m = -1        Now that you know the slope, plug it into the equation

y = mx + b

y = -1x + b   or   y = -x + b    To find b, plug in either one of the points into the equation, it doesn't matter which you use. I will use (5, 9)

9 = -(5) + b        Add 5 on both sides to get "b" by itself

9 + 5 = -5 + 5 + b

14 = b

y = -x + 14