Respuesta :
Answer:
y=-2x+2 (if you need it in y-intercept form)
2x+y=2 (if you need it in standard form)
Step-by-step explanation:
1. Write the original line in y=mx+b form. In other words, get the y by itself on the left side of the equation.
Subtract 2x from both sides.
y=-2x+1
2. Recall that parallel lines have the same slope. Slope is always the number with the x in the equation. Since the slope in the first equation is -2, the slope of the new line will also be -2.
3. Find the y-intercept. Use the point (-1,4) and plug the y and x values into the point-slope formula. M represents the slope.
y-y1=m(x-x1)
y-4=-2(x+1)
Simplify the equation.
y-4=-2x-2
y=-2x+2
(Proceed to step 4 if you need it in standard form)
4. Write the equation in standard form (x+y=z). Z represents the number by itself without variables.
Add -2x to both sides
2x+y=2
Answer:
An of line that passes through the point (−1,4) and is parallel to the line will be:
- [tex]y=-2x+2[/tex]
Step-by-step explanation:
We know that the slope-intercept form of the line equation
y = mx+b
where m is the slope and b is the y-intercept
Given the line
2x+y=1
converting the line into slope-intercept form
y = -2x+1
comparing with the slope-intercept form of the line equation
The slope of the line = m = -2
We know that the parallel lines have the same slopes.
Thus, the slope of line that passes through the point (−1,4) and is parallel to the line will 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, 4)
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-4=-2\left(x-\left(-1\right)\right)[/tex]
Add 4 to both sides
[tex]y-4+4=-2\left(x+1\right)+4[/tex]
[tex]y=-2x+2[/tex]
Therefore, an of line that passes through the point (−1,4) and is parallel to the line will be:
- [tex]y=-2x+2[/tex]
