Answer:
The line equation in slope-intercept form is:
[tex]y\:=-\frac{2}{5}x+4[/tex]
Hence, option D is true.
Step-by-step explanation:
Given the points
Finding the slope between the points
[tex]\left(x_1,\:y_1\right)=\left(0,\:4\right),\:\left(x_2,\:y_2\right)=\left(5,\:2\right)[/tex]
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{2-4}{5-0}[/tex]
[tex]m=-\frac{2}{5}[/tex]
As the y-intercept is obtained by setting the value x = 0.
As we know that when x = 0, the vale of y-intercept y = 4
so the y-intercept is b = 4.
As the slope-intercept form is
substituting the slope m = -2/5 and the y-intercept b=4
[tex]y = mx+b[/tex]
[tex]y\:=-\frac{2}{5}x+4[/tex]
Therefore, the line equation in slope-intercept form is:
[tex]y\:=-\frac{2}{5}x+4[/tex]
Hence, option D is true.
