Answer:
The equation of the line that is parallel to the linear graph of y = 2x - 1 and passes through the point (-1, 1) will be:
[tex]y=2x+3[/tex]
Hence, option D is true.
Step-by-step explanation:
We know that linear function can be represented using the slope-intercept formula
y = mx+b
where m is the slope and b is the y-intercept
Given the equation
y = 2x - 1
comparing with the slope-intercept form y = mx+b
Hence, the slope of the line y = 2x - 1 is: m = 2
We know that the parallel lines have the same slopes.
Thus, the slope of the equation of the line that is parallel to the linear graph of y = 2x - 1 will also be: 2
Using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope of the line and (x₁, y₁) is the point
substituting the values of the slope = 2 and the point (-1, 1)
[tex]y-1=2\left(x-\left(-1\right)\right)[/tex]
[tex]y-1=2\left(x+1\right)[/tex]
Add 1 to both sides
[tex]y-1+1=2\left(x+1\right)+1[/tex]
Simplify
[tex]y=2x+3[/tex]
Therefore, the equation of the line that is parallel to the linear graph of y = 2x - 1 and passes through the point (-1, 1) will be:
[tex]y=2x+3[/tex]
Hence, option D is true.
