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To find the equation of line A, we'll use the information provided:

1. Line A passes through the point \( (5, 17) \).
2. Line A is parallel to the line described by the equation \( y = 3x + 7 \).

Since line A is parallel to \( y = 3x + 7 \), it must have the same slope, \( m = 3 \).

The equation of a line in slope-intercept form is \( y = mx + c \). We already know \( m = 3 \) and we have a point through which the line passes, \( (5, 17) \). We can substitute these values into the equation to solve for \( c \):

\[
17 = 3(5) + c
\]

\[
17 = 15 + c
\]

\[
c = 2
\]

Therefore, the equation of line A is:

\[
y = 3x + 2
\]

Would you like to know more about this topic or have any other questions? Here are some related questions you might find interesting:

1. How would you find the equation of a line perpendicular to \( y = 3x + 7 \) that passes through the point \( (5, 17) \)?
2. What happens to the graph of the line if \( c \) is increased or decreased?
3. How can you determine the point where two lines intersect?
4. What is the significance of the slope in the equation of a line?
5. How can the distance from a point to a line be calculated?

**Tip**: Always verify your solution by plugging the coordinates of the point back into the equation to ensure that they satisfy the equation.

Line A passes through the point (5, 17) and is parallel to the line given by y = 3x + 7. What is the equation of line A? Give your answer in the form y = mx + c, where m and c are integers or fractions in their simplest forms.

This problem covers how to find the equation of a line parallel to y = 3x + 7 that passes through the point (5, 17). Learn about key algebraic concepts like the slope-intercept form and how to solve for the y-intercept. Suitable for Grades 8-10.

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