#10 Answer:
y = -5x + 7
Step-by-step explanation:
A line that is parallel will have the same slope. Then, we can use the given coordinate point to write a point-slope form equation. After that, we will rewrite the equation in the same form as the given equations. This looks to be a slope-intercept form equation, but with a coefficient on y to avoid fractions.
Given:
y = -5x + 4 at the point (1, 2)
Parallel lines, same slope:
m = -5
Point-slope form equation:
y - y1 = m(x - x1)
y - 2 = -5(x - 1)
Distribute and add 2 to both sides:
y = -5x + 5 + 2
Addition:
y = -5x + 7
#12 Answer:
2y = 3x - 16
Step-by-step explanation:
We will follow the same steps as above to find the parallel line through the given point.
Given:
2y = 3x + 10 at the point (2, -5)
Parallel lines, same slope:
m = 3/2
Point-slope form equation:
y - y1 = m(x - x1)
y - - 5 = 3/2(x - 2)
Simplify and distribute:
y + 5 = 3/2x - 3
Subtract 5 from both sides:
y = 3/2x - 8
Multiply both sides by 2 to remove the fraction:
2y = 3x - 16
