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
- Determine the line equation, in slope-intercept form, that is parallel to the given line and passes through a point https://brainly.com/question/1473992
- The midpoint https://brainly.com/question/3269852
- Determine the equation represents a line that passes through (–2, 4) and has a slope of 1 https://brainly.com/question/4819659
Keywords: which, two points lie on the line, the slope, gradient, the equation, the slope-intercept form, standard form
