1. which two points lie on a line with slope 2/3?
a. (2, 0) and (3,0)
b. (3, –4) and (1, 2)
c. (0, 0) and (2, 3)
d. (–3, 2) and (0, 4)
2. what is the slope of the line that passes through the given points?
(6, –1) and (–3, –1)
a. undefined
b. 0
c. – 2/3
d. – 3/2
4. write the equation in slope-intercept form. what are the slope and y-intercept?
3/4x + 4/5y = 4
a. y = 15/16x + 5; slope: 5; y-intcerpt: 15/16
b. y = 15/16x – 5; slope: 15/16 : y-intercept: –5
c. y = –15/16x – 5; slope: –15/16; y-intercept: –5
d. y = –15/16x + 5; slope: –15/16; y-intercept: 5

1. D

2.B

4.D

Problem 1

The formula for calculating slope or gradient of the line that passes through the given points is given by

Let's find out the slope of each option until we find the slope of ²/₃.

It corrects, this is the answer.

Problem 2

Given two points, i.e., (6, -1) and (-3, -1).

The formula for calculating slope or gradient of the line that passes through the given points is given by

Therefore, the slope is

Problem 4

Given which is a standard form.

Let us write the equation in slope-intercept form with the coefficient m as a gradient and k as y-intercept.

Both sides multiplied by ⁵/₄ so y becomes a subject.

Both sides subtracted by

This format is following the slope-intercept form, thus the slope is and y-intercept is 5.

Keywords: which, two points lie on the line, the slope, gradient, the equation, the slope-intercept form, standard form

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.