Question

A line has a slope of – 1 and passes through the point ( – 19,17). Write its equation in slope-intercept form.

Answer 1

`(\stackrel{x_1}{-19}~,~\stackrel{y_1}{17})\hspace{10em} \stackrel{slope}{m} ~=~ - 1 \\\\\\ \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}{17}=\stackrel{m}{- 1}(x-\stackrel{x_1}{(-19)}) \implies y -17 = - 1 ( x +19) \\\\\\ y-17=-x-19\implies {\Large \begin{array}{llll} y=-x-2 \end{array}}`

Answer 2

y = -x - 2

Explanation:

Pre-Solving

We are given that a line has a slope (m) of -1 and passes through (-19,17).

We want to write the equation of this line in slope-intercept form.

Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y intercept, hence the name

Solving

As we are already given the slope of the line, we can plug it into the equation.

Replace m with -1.

y = -1x + b

This can be rewritten to:

y = -x + b

Now, we need to find b.

As the equation passes through (-19,17), we can use its values to help solve for b.

Substitute -19 as x and 17 as y.

17 = -(-19) + b

17 = 19 + b

Subtract 19 from both sides.

-2 = b

Substitute -2 as b into the equation.

y = -x - 2