A. To find the equation of the line that passes through the points (-3, 7) and (-1, 11), you can start with the point-slope formula:
y - y₁ = m(x - x₁)
where (x₁, y₁) is one of the given points, and m is the slope of the line.
First, calculate the slope (m) using the two points (-3, 7) and (-1, 11):
m = (y₂ - y₁) / (x₂ - x₁) = (11 - 7) / (-1 - (-3)) = 4 / 2 = 2
Now that you have the slope (m), you can use one of the given points (let's use (-3, 7)) in the point-slope formula:
y - 7 = 2(x - (-3))
Simplify:
y - 7 = 2(x + 3)
Distribute the 2 on the right side:
y - 7 = 2x + 6
Now, isolate y by adding 7 to both sides:
y = 2x + 6 + 7
y = 2x + 13
So, the equation of the line that passes through the points (-3, 7) and (-1, 11) in slope-intercept form is:
y = 2x + 13
Equation of the Line:
y = 2x + 13
B. To find the equation of a line parallel to the given line (y = -3x - 1) and passing through the point (2, 4), you can start with the point-slope formula:
y - y₁ = m(x - x₁)
where (x₁, y₁) is the given point (2, 4), and (m) is the slope of the line.
Since you want a line parallel to (y = -3x - 1), the slope of the new line will be the same as the slope of (y = -3x - 1), which is -3.
Now, plug in the values:
y - 4 = -3(x - 2)
Simplify:
y - 4 = -3x + 6
Add 4 to both sides to isolate (y):
y = -3x + 6 + 4
y = -3x + 10
So, the equation of the line that is parallel to (y = -3x - 1) and passes through the point (2, 4) in slope-intercept form is:
y = -3x + 10