Which equation represents the line that passes through
the points (2, -1) and (6, 7)?
A y=x-2
y = 2x - 4
C y = 2x - 3
y = 2x - 5
B
D

y = 2x - 5

Step-by-step explanation:

The equation that represents the line that passes through the points (2, -1) and (6, 7) can be gotten by

Step 1

Finding the slope of the line

m = (y2 - y1) / (x2 - x1)

Points on lines are represented as coordinates (x, y)

We are given two points

Point 1 has coordinates (2, -1) which corresponds to (x2, y2)

Point 2 has coordinates (6, 7) which corresponds to (x1, y1)

Therefore,

x2= 2

y2 = -1

x1 = -6

y1 = 7

The slope,

m = (-1 - 7) / (2 - 6)

m = -8 / -4

m = 2

Step 2

The slope of a line can be gotten between any two points on the line and it is equal at any two points on the same line.

Let us assume a third point on the line has coordinates (x, y)

And given one point on the line with coordinates (6, 7)

Since, the slope of a line can be gotten between any two points and is equal, then we can say

m = (-1 - 7) / (2 - 6) = (y - 7) / (x - 6)

m = 2 = (y - 7) / (x - 6)

2 = (y - 7) / (x - 6)

Step 3

2 = (y - 7) / (x - 6)

Cross multiply

y - 7 = 2(x - 6)

y - 7 = 2x - 12

Step 4

Make y subject of formula by adding 7 to both sides of the equation

y - 7 + 7 = 2x - 12 + 7

y = 2x - 5

Step 5

y = 2x - 5 is the slope-intercept form equation of the line.

b

step-by-step explanation:

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be