Join the conversation on IDNLearn.com and get the answers you seek from experts. Get comprehensive answers to all your questions from our network of experienced experts.

Determine the equation of the line passing through the point (3, 17) with a slope of [tex]$m = 6$[/tex].

Equation of the line:


Sagot :

To determine the equation of the line passing through the point (3, 17) with a slope of 6, follow these steps:

1. Recall the Slope-Intercept Form: The equation of a line in slope-intercept form is given by:
[tex]\[ y = mx + b \][/tex]
where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.

2. Plug in the Slope (m): Here, the slope [tex]\( m \)[/tex] is given as 6. So, the equation becomes:
[tex]\[ y = 6x + b \][/tex]

3. Use the Given Point (3, 17): The line passes through the point (3, 17), meaning when [tex]\( x = 3 \)[/tex], [tex]\( y = 17 \)[/tex]. Substitute these values into the equation to find the y-intercept [tex]\( b \)[/tex]:
[tex]\[ 17 = 6 \cdot 3 + b \][/tex]

4. Solve for [tex]\( b \)[/tex]:
[tex]\[ 17 = 18 + b \][/tex]
To isolate [tex]\( b \)[/tex], subtract 18 from both sides:
[tex]\[ 17 - 18 = b \][/tex]
[tex]\[ -1 = b \][/tex]

5. Construct the Equation: Now that we have the slope [tex]\( m = 6 \)[/tex] and the y-intercept [tex]\( b = -1 \)[/tex], the equation of the line is:
[tex]\[ y = 6x - 1 \][/tex]

So, the equation of the line passing through the point (3, 17) with a slope of 6 is:
[tex]\[ y = 6x - 1 \][/tex]