Question

What is the equation of the line that is parallel to the linear graph of y = 2x - 1 and passes through the point (-1, 1)?

Answer 1

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:

$y=2x+3$

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

$y-y_1=m\left(x-x_1\right)$

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)

$y-1=2\left(x-\left(-1\right)\right)$

$y-1=2\left(x+1\right)$

Add 1 to both sides

$y-1+1=2\left(x+1\right)+1$

Simplify

$y=2x+3$

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:

$y=2x+3$

Hence, option D is true.