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=(y_2-y_1)/(x_2-x_1)` And substitute/plug in the two points

(5, 9) = (x₁, y₁)

(9, 5) = (x₂, y₂)

`m=(y_2-y_1)/(x_2-x_1)`

`m=(5-9)/(9-5)`

`m=(-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