Mathematics, 18.11.2020 14:00, kennethDA19

Which equation represents a line that passes through the two points in the
table?

Answers: 3

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answered: irene003

The equation that represents the line that passes through the given points is y - 1 = $\frac{5}{3}$ (x - 3) ⇒ A

Step-by-step explanation:

The point-slope form of the linear equation is y - y1 = m(x - x1), where

m is the slope of the line(x1, y1) is a point on the line

The rule of the slope is m = $\frac{y2-y1}{x2-x1}$ , where

(x1, y1) and (x2, y2) are two points on the line

∵ The line passes through points (3, 1) and (6, 6)

∴ x1 = 3 and y1 = 1

∴ x2 = 6 and y2 = 6

→ Substitute them in the rule of the slope to find it

∵ m = $\frac{6-1}{6-3}=\frac{5}{3}$

∴ m = $\frac{5}{3}$

→ Substitute the value of x1, y1, and m in the form of the equation above

∵ y - 1 = $\frac{5}{3}$ (x - 3)

∴ The equation that represents the line that passes through the given

points is y - 1 = $\frac{5}{3}$ (x - 3)

answered: Guest

$y> \frac{1}{3}x$ and y≤ -x +4 .

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 = $\frac{1-0}{3-0} = \frac{1}{3}$ .

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

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

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

$y> \frac{1}{3}x$ .

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

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

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

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

answered: Guest

it is not that hard all u have to do is plot the graph

step-by-step explanation:

Need with this if u can answer the question comment it

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