Find the equation of a line that passes through (2,11) and is parallel to the graph of y=4x+5. Wrote the equation in slope-intercept form, if possible.

y = 4x + 3

Step-by-step explanation:

Two lines are parallel if they have the same slope.

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

Line 1 has a slope of 4. Let's say the slope of line 1 is m₁

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.

Since line 1 and line 2 are parallel, their slope is the same, m₁ = m₂.

m₂ = 4

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:

where:

y₁ = y coordinate of the point

x₁ = x coordinate of the point

m = slope of the line

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:

simplifying the equation and converting it to slope-intercept form

sine

step-by-step explanation: