Identify the Line Equation with Slope 9y Passing Through (-5, -8)

Question

A straight line with the slope 9 passes through the point (5,8) (-5,-8) .

Which of the following equations corresponds to the line?

Video Solution

Solution Steps

00:00 Find the algebraic representation of the function
00:03 We'll use the straight line equation
00:09 We'll substitute the point according to the given data
00:15 We'll substitute the slope according to the given data
00:19 We'll continue solving to find the intersection point
00:30 We'll isolate intersection point B
00:36 This is the intersection point with the Y-axis
00:41 Now we'll substitute the intersection point and slope in the line equation
00:53 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the given information
  • Step 2: Apply the point-slope formula
  • Step 3: Convert to slope-intercept form and verify against the given choices

Now, let's work through each step:
Step 1: The problem states the line passes through point (5,8)(-5, -8) and has a slope of 99.
Step 2: Using the point-slope form equation, yy1=m(xx1)y-y_1 = m(x-x_1), plug in (x1,y1)=(5,8)(x_1, y_1) = (-5, -8) and m=9m = 9. So the equation becomes:

y(8)=9(x(5)) y - (-8) = 9(x - (-5))

Which simplifies to:

y+8=9(x+5) y + 8 = 9(x + 5)

Simplifying further gives:

y+8=9x+45 y + 8 = 9x + 45

Then, bring the 88 to the right side to solve for yy in terms of xx:

y=9x+458 y = 9x + 45 - 8 y=9x+37 y = 9x + 37

Therefore, the equation of the line in slope-intercept form is y=9x+37y = 9x + 37, which corresponds to choice 11.

Therefore, the solution to the problem is y=9x+37y = 9x + 37.

Answer

y=9x+37 y=9x+37