Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Find the intersection point of the line [tex] y = x - 3 [/tex] with the point [tex] A(9,12) [/tex].

Sagot :

Sure, let's solve the problem step by step.

We have a point [tex]\( A \)[/tex] with coordinates [tex]\( (9,12) \)[/tex] and the equation of a line given by [tex]\( y = x - 3 \)[/tex].

Step 1: Understand the Equation of the Line

The equation of the line is [tex]\( y = x - 3 \)[/tex]. This is a linear equation in slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m = 1 \)[/tex] (the slope) and [tex]\( b = -3 \)[/tex] (the y-intercept).

Step 2: Locate the Point on the Line Corresponding to the x-coordinate of A

The x-coordinate of point [tex]\( A \)[/tex] is [tex]\( 9 \)[/tex]. To find the corresponding y-coordinate on the line, we substitute [tex]\( x = 9 \)[/tex] into the line’s equation:
[tex]\[ y = 9 - 3 \][/tex]
[tex]\[ y = 6 \][/tex]

So, the point on the line with the same x-coordinate as [tex]\( A \)[/tex] is [tex]\( (9, 6) \)[/tex].

Step 3: Calculate the Difference in the y-coordinates

Now, we need to find the difference between the y-coordinate of point [tex]\( A \)[/tex] and the y-coordinate of the corresponding point on the line.

The y-coordinate of point [tex]\( A \)[/tex] is [tex]\( 12 \)[/tex].

The y-coordinate of the point on the line is [tex]\( 6 \)[/tex].

Thus, the difference in the y-coordinates is:
[tex]\[ 12 - 6 = 6 \][/tex]

So the point [tex]\( A \)[/tex] is 6 units above the corresponding point on the line.

Final Answer

Given the information provided and the steps outlined:
- The coordinates of point [tex]\( A \)[/tex] are [tex]\( (9, 12) \)[/tex].
- The coordinates of the corresponding point on the line are [tex]\( (9, 6) \)[/tex].
- The difference in the y-coordinates is [tex]\( 6 \)[/tex].

Thus, the detailed step-by-step solution confirms that:
[tex]\[ A = (9, 12) \][/tex]
[tex]\[ \text{Point on the line} = (9, 6) \][/tex]
[tex]\[ \text{Difference in y-coordinates} = 6 \][/tex]
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.