Question

Graph the following lines and write the equation in slope-intercept form. d Through the point (2,−4) with y-intercept of −2.

Answer 1

Check the picture below.

`\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{-4})\qquad \underset{y-intercept}{(\stackrel{x_2}{0}~,~\stackrel{y_2}{-2})} \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{2}}}\implies \cfrac{-2+4}{-2}\implies \cfrac{2}{-2}\implies -1`

`\bf \begin{array} \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}{(-4)}=\stackrel{m}{-1}(x-\stackrel{x_1}{2}) \\\\\\ y+4=-x+2\implies y=-x-2`

Answer 2

`y=-1x-2`

Explanation:

Equation of a line is
`y=mx+b`

where m is the slope and b is the y intercept

Through the point (2,−4) with y-intercept of −2.

Y intercept is -2, the value of b is -2

(2,−4) is (x1.y1) and b=-2

plug in the value in y=mx+b

`-4=m(2)-2`, solve for m

add 2 on both sides

`-2=m(2)`

divide 2 on both sides

m=-1

Equation of the line is

`y=-1x-2`

Graph the equation using point (2,-4) and y intercept (0,-2)

the graph is attached below