write the equation of each line using the given information.
a. the points (2,1.5) and (−5,36.5) both lie on the line.
b. m=4 and the point (3,15) lies on the line.
c. it has the same slope as y=1 and passes through (3,−8).
d.m=2and it has a y-intercept of (0,4).

a. 10x + 2y = 23

b. 4x - y + 3 = 0

c. y + 8 = 0

d. 2x - y + 4 = 0

Step-by-step explanation:

a.

Slope of the line 'm' is = = -5

Equation of the line with slope m and passing through the point (x₁,y₁) is y-y₁ = m·(x-x₁)

⇒y-1.5 = -5·(x-2)

⇒y = -5x + 10 + 1.5

⇒5x + y = 11.5 (or) 10x + 2y = 23

b.

Slope of the line 'm' = 4

Equation of the line with slope m and passing through the point (x₁,y₁) is y-y₁ = m·(x-x₁)

⇒y-15 = 4·(x-3)

⇒y = 4x -12 + 15

⇒4x - y + 3 = 0

c.

Line is parallel to y = 1

Equations of parallel lines only differ by constant. So the required line equation has the form y = c where c is any real number.

But, it is given that the line passes through the point (3,-8)

⇒c=-8

⇒y = -8 (or) y + 8 = 0

d.

Equation of a line with slope 'm' and y-intercept of (0,c) is of the form y = mx + c

⇒y = 2x + 4

⇒2x - y + 4 = 0