Answer:
y = 4x + 3
Step-by-step explanation:
Two lines are parallel if they have the same slope.
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Let's say the line y = 4x + 5 is line 1.
Line 1 is in the form of y = mx + b (slope-intercept form)
where:
m = slope
b = y-intercept
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Line 1 has a slope of 4. Let's say the slope of line 1 is m₁
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The problem says the we need to find a line that is parallel to line 1 and passing through point (2, 11). Let's say the line we want to find is Line 2 and it's slope is m₂.
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Since line 1 and line 2 are parallel, their slope is the same, m₁ = m₂.
m₂ = 4
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Since line 2 is passing through a point, we can use the point-slope form of a line to determine the equation of the line.
Point-slope form of a line:
[tex]\mathsf{y-y_1=m(x-x_1)}[/tex]
where:
y₁ = y coordinate of the point
x₁ = x coordinate of the point
m = slope of the line
[tex]\\[/tex]
For the line 2, the coordinates of the point is (2, 11). x₁ = 2 and y₁ = 11.
Substituting all the values we have in the point-slope form:
[tex]\mathsf{y-11=4(x-2)}[/tex]
simplifying the equation and converting it to slope-intercept form
[tex]\mathsf{y-11=4x-8}[/tex]
[tex]\mathsf{y=4x-8+11}[/tex]
[tex]\mathsf{y=4x+3} \longleftarrow \textsf{\textbf{ANSWER}}[/tex]
