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.
bro help a homie out, please
parallel means the slope is the same
plug in the given point to find the intercept
y = 4 x + b ... 7 = (2 * 4) + b
To find the equation of a line that is parallel to another line, we need to use the fact that parallel lines have the same slope. The given line has a slope of 4.
Using the point-slope formula, which states that the equation of a line passing through a point (x₁, y₁) with slope m is given by y - y₁ = m(x - x₁), we can substitute the values (2,7) and m = 4 into the formula to find the equation of the line:
y - 7 = 4(x - 2)
Simplifying:
y - 7 = 4x - 8
Rearrange the equation to the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept:
y = 4x - 8 + 7
y = 4x - 1
So, the equation of the line that passes through the point (2,7) and is parallel to the line y = 4x + 1 is y = 4x - 1.