Answer: B) increasing for x < -4/3 and x > 4/3
decreasing for -4/3 < x < 4/3
<u>Step-by-step explanation:</u>
Graph the equation and follow the curve from left to right. If you are going up, it is increasing. If you are going down, it is decreasing.
Refer to the image below. Red is increasing. Blue is decreasing.
The vertices are at: x = -4/3 and x = 4/3
The point slope form of the line which passes through the points and
is
i.e.,
.
Further explanation:
It is given that line passes through the points and
.
The objective is to determine the point slope form of the line which passes through the points and
.
The options given are as follows:
Option A: 2x-5y=-15
Option B: 2x-5y=-17
Option C: 2x+5y=-15
Option D: 2x+5y=-17
Consider the point as
and
as
.
Slope of a curve is defined as the change in the value of with respect to change in value of
.
The slope of the line is calculated as follows:
To obtain the value of slope substitute the value of in the above equation.
Therefore, the slope of the line is
The general way to express the equation of a line in its point slope form is as follows:
To obtain the point slope form of the equation of the line substitute the value of ,
and
in the above equation.
From the above calculation it is concluded that the point slope form the equation of a line is
Figure 1 (attached in the end) represents the graph of the function .
This implies that the correct option for the point slope form of the line is option C.
Therefore, the point slope form of the line which passes through the points and
is
i.e., option C.
Learn more:
1. A problem to complete the square of quadratic function brainly.com/question/12992613
2. A problem to determine the slope intercept form of a line brainly.com/question/1473992
3. Inverse function brainly.com/question/1632445.
Answer details
Grade: High school
Subject: Mathematics
Chapter: Linear equation
Keywords: Equation, linear equation, slope, intercept, x-intercept, y-intercept, intersect, graph, curve, slope intercept form, line, y=3x/2-3, standard form, point slope form.
