Answer:
A. Slope = 3
B. y-intercept = 1
C. Slope-Intercept Form is y = 3x + 1
D. Standard Form is -3x + y = 1
Step-by-step explanation:
A.
Given two points [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex], we define the slope as:
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
This is the rate of change of a function (line).
Given the two points, we find the slope to be:
[tex]\frac{y_2-y_1}{x_2-x_1}\\=\frac{7-(-2)}{2-(-1)}\\=\frac{7+2}{2+1}\\=\frac{9}{3}\\=3[/tex]
Thus,
The slope is 3
B.
Slope-Intercept form of a line is y = mx + b
Where m is slope and b is the y-intercept
We plug in 3 into m, and use one point given (such as (2,7) and place 2 into x and 7 into y, and solve for b (the y-intercept). Shown below:
[tex]y=mx+b\\7=3(2)+b\\7=6+b\\b=7-6\\b=1[/tex]
Hence y-intercept is 1
C.
The slope intercept form of a line is y = mx + b
Where m is the slope
b is the y -intercept (the place in graph where the line cuts the y-axis)
Now, we know m = 3 (from A)
and b = 1 (from B)
Now, we put these into the slope-intercept form of a line and get the equation as:
y = mx + b
y = 3x + 1
D.
The standard form of a line is given by Ax + By = C
So we need to keep the x and y on the left side and take the constant to the right side. Let's convert slope intercept form (from part C) to standard form:
y = 3x + 1
-3x + y = 1
