Answer:
[tex]y=-2x+2[/tex]
Step-by-step explanation:
Hi there!
Slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)
1) Determine the slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where the two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (-1, 4) and (0, 2)
[tex]=\frac{2-4}{0-(-1)}\\=\frac{-2}{0+1}\\=\frac{-2}{1}\\= -2[/tex]
Therefore, the slope of the line is -2. Plug this into [tex]y=mx+b[/tex]:
[tex]y=-2x+b[/tex]
2) Determine the y-intercept
[tex]y=-2x+b[/tex]
Recall that the y-intercept is the value of y when the line crosses the y-axis, meaning that the y-intercept occurs when x is equal to 0.
One of the given points is (0,2). Notice how y=2 when x=0. Therefore, the y-intercept of the line is 2.
Plug this back into the equation:
[tex]y=-2x+2[/tex]
I hope this helps!
