Write an equation in slope-intercept form for the line that is parallel to the given line and passes through the given point.
π¦ = 4π₯ + 6, (2, 7)
Y = mx+b
Y = 4x+6
7 = 4*2+b
7 = 8+b
b = -1.
Y = 4x+b.
Y = 4x-1.
Well, I could take the serious approach and give you the equation right away, but where's the fun in that, right? Let's add a touch of humor to your equation!
To find a line parallel to π¦ = 4π₯ + 6, we know the slope must be the same because parallel lines have the same slope. So the new line also has a slope of 4.
Now, let's find the equation in slope-intercept form. We already know the slope, so we just need to find the value of the y-intercept. We have the point (2, 7), which means that when x = 2, y = 7.
Since we have x, y, and the slope, we can use the good old slope-intercept form (π¦ = ππ₯ + π) and substitute in our values:
7 = 4(2) + π
Simplifying that, we get:
7 = 8 + π
Subtracting 8 from both sides:
-1 = π
So the equation for the line parallel to π¦ = 4π₯ + 6 and passing through the point (2, 7) is:
π¦ = 4π₯ - 1.
And there you have it! A line that will make mathematicians laugh with its brilliance and humor.
To find the equation of a line that is parallel to the given line π¦ = 4π₯ + 6 and passes through the given point (2, 7), we need two pieces of information: the slope of the given line and the coordinates of the given point.
The given line is in slope-intercept form, which is π¦ = ππ₯ + π, where π represents the slope and π represents the y-intercept.
We can observe that the slope of the given line is 4. Since a line parallel to the given line will have the same slope, the slope of our new line will also be 4.
Now, we can use the point-slope form of a linear equation, which is π¦ β π¦β = π(π₯ β π₯β), where (π₯β, π¦β) represents the coordinates of the given point and π represents the slope.
Plugging in the values we have, we get:
π¦ β 7 = 4(π₯ β 2)
Now, let's simplify the equation:
π¦ β 7 = 4π₯ β 8
To put the equation in slope-intercept form, we isolate y:
π¦ = 4π₯ β 8 + 7
π¦ = 4π₯ β 1
So, the equation in slope-intercept form for the line that is parallel to π¦ = 4π₯ + 6 and passes through the point (2, 7) is π¦ = 4π₯ β 1.
To find an equation of a line that is parallel to the given line π¦ = 4π₯ + 6, we need to use the fact that parallel lines have the same slope.
The given line has a slope of 4, so any line that is parallel to it will also have a slope of 4.
We also have a point that the parallel line needs to pass through, which is (2, 7).
To write an equation in slope-intercept form (π¦ = ππ₯ + π), we can substitute the slope (π = 4) and the coordinates of the point (π₯ = 2, π¦ = 7) into the equation and solve for π, which represents the y-intercept.
Let's follow the steps:
Step 1: Substitute π = 4, π₯ = 2, and π¦ = 7 into the equation π¦ = ππ₯ + π:
7 = 4(2) + π
Step 2: Simplify the equation:
7 = 8 + π
Step 3: Isolate π by subtracting 8 from both sides of the equation:
-1 = π
The value of π is -1.
Therefore, the equation of the line parallel to π¦ = 4π₯ + 6 and passing through the point (2, 7) is:
π¦ = 4π₯ - 1