Question

Write equation of the line containing (4,2) and (3,5) in slope-intercept form.

Answer 1

Answer:

The equation of the line containing (4,2) and (3,5)  in the slope-intercept form will be:

• y=-3x+14

Step-by-step explanation:

Given the points

• (4, 2)

• (3, 5)

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(4,\:2\right),\:\left(x_2,\:y_2\right)=\left(3,\:5\right)$

$m=\frac{5-2}{3-4}$

$m=-3$

We know that the slope-intercept form of the line equation is

$y=mx+b$

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

$y=mx+b$

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.

$y=mx+b$

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:

• y=-3x+14