Answer:
The distance is [tex]\sqrt{20}[/tex] or [tex]2\sqrt{5}[/tex].
Step-by-step explanation:
Slope of parallel: 2
Slope of perpendicular: -1/2
Pick a point for y =2x + 7. For example (0,7)
Use the perpendicular slope to get to the other line to find the other point of y=2x-3. Look at the screenshot...I got (4,5).
Distance formula [tex]\sqrt{(x_{2}-x_{1} )^{2}+(y_{2} -y_{1})^2 }[/tex]
Insert (0,7) and (4,5)
[tex]\sqrt{(0-4)^{2}+(7-5)^2 }[/tex] = [tex]\sqrt{(-4)^{2}+(2)^2 } = \sqrt{(16)+(4)} } = \sqrt{20} = 2\sqrt{5}[/tex]
The distance between parallel lines whose equations are y = 2x + 7 and y = 2x – 3 is [tex]2\sqrt{5}[/tex] and can be determined by using the point-slope form and also by using the distance formula.
Given :
First, determine the line perpendicular to the line (y = 2x + 7) whosw slope is -1/2 and intersect the line (y = 2x + 7) at point (0,7).
Using the point-slope, the equation of the perpendicular line can be determined.
[tex](y-y_1)=m(x-x_1)[/tex] ---- (1)
where m is the slope and [tex](x_1,y_1)[/tex] is the point on the line.
Now, put the value of known terms in the equation (1).
[tex]y-7=-\dfrac{1}{2}(x-0)[/tex]
y = -0.5x + 7 --- (2)
Now, determine the point of intersection between lines (y = -0.5x + 7) and (y = 2x -3).
Substitute the value of y that is (y = 2x - 3) in equation (y = -0.5x + 7).
2x - 3 = -0.5x + 7
2.5x = 10
x = 4
Now, put the value of x in the equation (y = -0.5x + 7).
y = -0.5(4) + 7
y = 5
Now, the distance between two points is given by the equation:
[tex]\rm D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\rm D = \sqrt{(0-4)^2+(7-5)^2}[/tex]
[tex]\rm D = \sqrt{20}[/tex]
[tex]\rm D = 2\sqrt{5}[/tex]
The distance between parallel lines whose equations are y = 2x + 7 and y = 2x – 3 is [tex]2\sqrt{5}[/tex].
For more information, refer to the link given below:
https://brainly.com/question/19707745
