Question

Write an equation passing through the point and PARALLEL to the given line.

(4,7): y = 3
a) y = 7
b) y = 4x + 7
c) y = 3x
d) y = 4

Answer 1

The equation of the line passing through the point (4,7) that is parallel to the line y = 9 + 3x is y = 3x - 5.

Step-by-step explanation:

The question involves finding an equation of a line passing through the point (4,7) which is parallel to the given line y = 9 + 3x. To be parallel, the new line must have the same slope, which is 3. The general form of the equation of a line is y = mx + b where m is the slope and b is the y-intercept. Since we know the slope is 3, we only need to find the y-intercept that will allow the line to pass through the point (4,7). We can substitute the point values into the equation to get 7 = 3(4) + b, which simplifies to 7 = 12 + b. Solving for b, we get b = -5. Therefore, the equation of the line passing through (4,7) parallel to y = 9 + 3x is y = 3x - 5.