Answer:
The equation of the line containing (4,2) and (3,5) in the slope-intercept form will be:
Step-by-step explanation:
Given the points
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(4,\:2\right),\:\left(x_2,\:y_2\right)=\left(3,\:5\right)[/tex]
[tex]m=\frac{5-2}{3-4}[/tex]
[tex]m=-3[/tex]
We know that the slope-intercept form of the line equation is
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept
substituting m=-3 and the point (4, 2) to get the y-intercept i.e. b
[tex]y=mx+b[/tex]
2=(-3)4 + b
2 = -12 + b
b = 2+12
b = 14
Now, substituting b=14 and m=-3 in the slope-intercept form to determine the equation of a line in the slope-intercept.
[tex]y=mx+b[/tex]
y=(-3)x+(14)
y=-3x+14
Thus, the equation of the line containing (4,2) and (3,5) in the slope-intercept form will be:
