Question

What is the slope-intercept form of the equation of a line that passes through (1, –6) with a slope of 5?

Answer 1

`\bf (\stackrel{x_1}{1}~,~\stackrel{y_1}{-6})~\hspace{10em} \stackrel{slope}{m}\implies 5 \\\\\\ \begin{array}c \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{5}(x-\stackrel{x_1}{1}) \\\\\\ y+6=5x-5\implies y=5x-11`

Answer 2

Answer:
`y=5x-11`

Explanation:

The equation of the line in Slope-Intercept form is:

`y=mx+b`

Where "m" is the slope and "b" is the y-intercept

We know that the slope of this line is:

`m=5`

And its that passes through the point (1,-6), then we can substitute values into
`y=mx+b` and solve for "b":

`-6=5(1)+b\\\\-6-5=b\\\\b=-11`

Then, the equation of this line in Slope-Intercept form is:

`y=5x-11`