What is the equation of the line that passes through #(1, 5)# and #(-2, 14)# in slope-intercept form?

1 Answer
Demirari
Jul 6, 2017

#y = -3x + 8#

Explanation:

First, in order to solve this, we need to understand slope using two points. To put this simply in mathematical terms: #(y_2-y_1)/(x_2-x_1)#.

Let us say that #(-2, 14)# will be our #x_2, y_2# and #(1, 5)# as our #x_1, y_1#.

Plugging these variables into the slope formula shown previously: #(14-5)/(-2-1) = 9/-3 = -3#.

So we find that -3 is our slope, so using #y = mx + b#, we will replace #m# with #-3#, so it'll become #y = -3x + b#.

In order to solve for b, we will use either two points given to us in the question. Let's use #(-2, 14)#. So the point tells us that our x will equal -2 and our y will equal 14.

Thus: #14 = -3(-2) + b#.

Running through the calculation and we get #14 = 6 + b#.

Solving for b by subtracting 6 from both sides, we get #8 = b#.

So our slope-intercept form will be #y = -3x + 8#

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