1. Write the equation of a line in slope intercept form that is parallel to y = 3x - 2 and passes through the point (-2, 1)
y = -3x-5?
2. Write the equation of the line that passes through (2, 1) and is perpendicular to 5x + y = 9.
x + 5y = 3?
the slope must be 3, so using the point-slope form, you have
y-1 = 2(x+2)
y-1 = 2x+4
y = 2x+5
Or, you know that the line must be
y = mx+b
so plug in your point and you have
1 = 2(-2)+b
b = 5
so y = 2x+5
#2 5x+y=9 has slope -1/5
so, the perpendicular line has slope 5
y-1 = 5(x-2)
y-1 = 5x-10
5x-y = 9
Your equation is clearly not right, since plugging in (2,1) gives
2+5*1 = 3
which is false.
To find the equation of a line in slope-intercept form (y = mx + b), you need to know the slope (m) and the y-intercept (b).
1. We are given that the line we are looking for is parallel to the line y = 3x - 2. Since parallel lines have the same slope, our line will also have a slope of 3. To find the y-intercept, we'll use the point (-2, 1) that the line passes through.
Using the point-slope form of a line, which is y - y₁ = m(x - x₁), we can substitute the values (-2, 1) and m = 3:
y - 1 = 3(x - (-2))
y - 1 = 3(x + 2)
y - 1 = 3x + 6
y = 3x + 7
Therefore, the equation of the line parallel to y = 3x - 2 and passes through the point (-2, 1) is y = 3x + 7.
2. We are given the equation of the line 5x + y = 9 and asked to find a line that passes through the point (2, 1) and is perpendicular to this line. Perpendicular lines have negative reciprocal slopes, so we need to find the slope of the given line and then take its negative reciprocal.
Rewriting the equation in slope-intercept form: y = -5x + 9.
The slope of this line is -5.
To find the negative reciprocal of -5, we flip the fraction and change the sign: 1/(-5) = -1/5.
Using the point-slope form with the given point (2, 1) and slope -1/5:
y - 1 = (-1/5)(x - 2)
y - 1 = (-1/5)x + 2/5
To write the equation in slope-intercept form, we can multiply through by 5 to get rid of the fraction:
5(y - 1) = -x + 2
5y - 5 = -x + 2
5y = -x + 7
x + 5y = 7
Therefore, the equation of the line that passes through (2, 1) and is perpendicular to 5x + y = 9 is x + 5y = 7.