Question

Write the equation in slope-intercept form for the line that passes through (5, 4) and (6,-1).

SHOW YOUR WORK​

Answer 1

y = -5x + 29

Explanation:

Slope-Intercept Form of the Line

Given a line of slope m and y-intercept b, the equation of the line can be written as:

y = mx + b

The slope can be calculated by using the formula:

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

Where (x1,y1) and (x2,y2) are the points through which the line passes.

We are given the points (5,4) and (6,-1), thus:

`\displaystyle m=(-1-4)/(6-5)=(-5)/(1)=-5`

Now we use one of the points to find the value of b, for example (5,4):

4 = -5(5) + b

b = 25+4 = 29

Thus, the equation of the line is:

y = -5x + 29