Question

1. Which two points lie on a line with slope 2/3?

Answer 1

1. D

2.B

4.D

Further explanation

Problem 1

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

$\boxed{ \ m = \frac{y_2 - y_1}{x_2 - x_1} \ }$

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

$\boxed{ \ A. \ (2, 0) \ and \ (3, 0) \ } \rightarrow \boxed{ \ (x_1, y_1)\ and \ (x_2, y_2) \ }$

$\boxed{ \ m_A = \frac{0 - 0}{3 - 2} \ } = 0 \ }$

$\boxed{ \ B. \ (3, -4) \ and \ (1, 2) \ } \rightarrow \boed{ \ (x_1, y_1)\ and \ (x_2, y_2) \ }$

$\boxed{ \ m_B = \frac{2 - (-4)}{1 - 3} \ } = -3 \ }$

$\boxed{ \ C. \ (0, 0) \ and \ (2, 3) \ } \rightarrow \boxed{ \ (x_1, y_1)\ and \ (x_2, y_2) \ }$

$\boxed{ \ m_C = \frac{3 - 0}{2 - 0} \ } = \frac{3}{2} \ }$

$\boxed{ \ D. \ (-3, 2) \ and \ (0, 4) \ } \rightarrow \boxed{ \ (x_1, y_1)\ and \ (x_2, y_2) \ }$

$\boxed{\boxed{ \ m_D = \frac{4 - 2}{0 - (-3)} \ } = \frac{2}{3} \ }}$ It corrects, this is the answer.

Problem 2

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

$\boxed{ (x_1, y_1) = (6, -1) }$

$\boxed{ (x_2, y_2) = (-3, -1) }$

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

$\boxed{ \ m = \frac{y_2 - y_1}{x_2 - x_1} \ }$

$\boxed{ \ m = \frac{-1 - (-1)}{-3 - 6} \ }$

$\boxed{ \ m = \frac{0}{-9} \ }$

Therefore, the slope is $\boxed{\boxed{ \ m= 0 \ }}$

Problem 4

Given $\boxed{ \ \frac{3}{4}x + \frac{4}{5}y = 4 \ }$ which is a standard form.

Let us write the equation in slope-intercept form $\boxed{ \ y = mx + k \ }$ with the coefficient m as a gradient and k as y-intercept.

$\boxed{ \ \frac{3}{4}x + \frac{4}{5}y = 4 \ }$

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

$\boxed{ \ \frac{15}{16}x + y = 5 \ }$

Both sides subtracted by $\boxed{\frac{15}{16}x}$

$\boxed{ \ y = -\frac{15}{16}x + 5 \ }$

This format is following the slope-intercept form, thus the slope is $\boxed{\boxed{ \ -\frac{15}{16} \ }}$ and y-intercept is 5.

Learn more

1. Determine the line equation, in slope-intercept form, that is parallel to the given line and passes through a point  brainly.com/question/1473992
2. The midpoint brainly.com/question/3269852
3. Determine the equation represents a line that passes through (–2, 4) and has a slope of 1  brainly.com/question/4819659

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

Answer 2

1. D. (–3, 2) and (0, 4)
2. A. undefined
4. D. y = –15/16x + 5; slope: –15/16; y-intercept: 5
hope it helps