The equations are: A :y= -5x +11.5 B: y=4x+3 C.y=1 and D : y=4
Step-by-step explanation:
You can write the equations of the lines in the slope intercept form, y=mx+c where m is the slope of the line, and c is the y-intercept value of the line.
A.
The points ( 2 , 1 . 5 ) and ( − 5 , 36 . 5 ) both lie on the line.
finding the slope of the line using the points
slope, m=rise/run
rise=Δy=36.5-1.5=35
run=Δx=-5-2= -7
m= Δy/Δx= 35/-7 =-5
Equation of a the line, with m=-5 and point (2,1.5) in slope intercept form will be;
m=Δy/Δx = -5 =y-1.5/x-2
-5(x-2) = y-1.5
-5x+10=y-1.5
-5x+10+1.5=y
⇒⇒y= -5x +11.5 ------------ the equation of the line
B.
The slope m is given as 4 and point (3,15)
m=rise/run
m=Δy/Δx
4=y-15/x-3
4(x-3)= y-15
4x-12 = y-15
4x-12+15=y
4x+3=y
⇒⇒y=4x+3 -------------------the equation of the line in slope-intercept form
C.
The equation given is y=1, which is a horizontal line with y-intercept value as 1
The slope here is 0
Given points (3,-1) and m=0
m=Δy/Δx
0=y--1/x-3
0=y+1/x-3
0(x-3)=y+1
0=y+1
⇒⇒equation of line will be y=1
D.
Given slope of line as m=2, and the y-intercept at (0,4) then the equation will be
m=Δy/Δx
2=y-4/x-0
2(x-0)=y-4
0=y-4
y=4 ⇒⇒⇒⇒the equation of the line
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Equation of a line : https://brainly.com/question/8865631
Keyword : equation, line, points
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