Find the equation of the line that passes through the point (2.7) and is parallel to the line y=4x+1 . Write the equation using the slope-intercept form.
Please help, this makes no sense to me.
If this makes no sense, you need to review slope and the point-slope form.
y=4x+1 has slope m=4
Now you have a point and a slope, so the equation is
y-7 = 4(x-2)
now just rearrange things to slope-intercept form.
1000
To find the equation of a line that is parallel to y=4x+1 and passes through the point (2,7), we first need to find the slope of the given line.
The equation of the given line is in the form y=mx+b, where m represents the slope. From the given equation, we can see that the slope is 4.
Since parallel lines have the same slope, the slope of the line we are looking for is also 4.
Now that we have the slope (m=4) and a point (2,7) that the line passes through, we can use the point-slope form of a line to find the equation:
y - y1 = m(x - x1),
where (x1, y1) is the given point and m is the slope.
Plugging in the values, we have:
y - 7 = 4(x - 2).
Now, let's simplify the equation:
y - 7 = 4x - 8.
To rewrite the equation in slope-intercept form (y=mx+b), let's isolate y:
y = 4x - 8 + 7.
Simplifying further:
y = 4x - 1.
Therefore, the equation of the line that passes through (2,7) and is parallel to the line y=4x+1 is y = 4x - 1.
To find the equation of a line parallel to another line, we need to use the fact that parallel lines have the same slope. In this case, the given line has a slope of 4, so our target line will also have a slope of 4.
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. Since we now know the slope, we just need to find the y-intercept.
To find the y-intercept, we can use the point-slope formula: y - y₁ = m(x - x₁), where (x₁, y₁) is the given point (2, 7). Plugging in the values, we get:
y - 7 = 4(x - 2).
Now, we can simplify this equation by distributing 4 to both terms inside the parentheses:
y - 7 = 4x - 8.
Next, let's isolate y by adding 7 to both sides of the equation:
y = 4x - 8 + 7.
Simplifying further, we have:
y = 4x - 1.
Therefore, the equation of the line parallel to y = 4x + 1 and passing through the point (2, 7) is y = 4x - 1 in slope-intercept form.