Write the equation of the line that goes through the point (6, 5) and is perpendicular to the line y = 3x + 8.
What is the slope of y = 3x + 8? __
m = __
Since your line is perpendicular to y = 3x + 8, your slope has the opposite sign and reciprocal (flip the fraction) slope. "M" your line = __
Use your slope and given point to solve for "b" and write the equation.
the slope of y = 3x + 8 is 3
so the slope of the perpendicular line is -1/3
new line must be y = (-1/3)x + b , with (6,5) lying on it, so
5 = (-1/3)(6) + b
5 = -2 + b
b = 7
looks like y = (-1/3)x + 7
Thanks for your help mathhelper
The slope of the line y = 3x + 8 is 3. Since your line is perpendicular to this line, the slope of your line will be the opposite sign and reciprocal of 3. Therefore, the slope of your line, denoted as "m", will be -1/3.
Using the point (6, 5) and the slope (-1/3), we can use the point-slope form of a linear equation to solve for "b", which represents the y-intercept.
The point-slope form of a linear equation is given as:
y - y1 = m(x - x1),
Where (x1, y1) represents the coordinate of the given point, and "m" represents the slope.
Plugging in the values, we have:
y - 5 = (-1/3)(x - 6).
Simplifying the equation further:
y - 5 = (-1/3)x + 2.
To obtain the equation in slope-intercept form (y = mx + b), we isolate y by adding 5 to both sides:
y = (-1/3)x + 2 + 5.
Simplifying:
y = (-1/3)x + 7.
Therefore, the equation of the line that goes through the point (6, 5) and is perpendicular to the line y = 3x + 8 is y = (-1/3)x + 7.
To find the slope of the line y = 3x + 8, we can compare it to the standard slope-intercept form y = mx + b, where m represents the slope. In this case, we can see that the slope (m) is 3.
Since your line is perpendicular to the line y = 3x + 8, we know that the slopes of the two lines are negative reciprocals of each other. The negative reciprocal of 3 would be -1/3. So, the slope (m) of the desired line is -1/3.
Now that we have the slope, we can use the given point (6, 5) to find the y-intercept (b). We can start by using the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is the given point.
Plugging in the values, we get:
y - 5 = (-1/3)(x - 6)
Next, we can distribute the -1/3 to the terms inside the parentheses:
y - 5 = (-1/3)x + 2
To isolate y, we can add 5 to both sides of the equation:
y = (-1/3)x + 2 + 5
Simplifying further, we get:
y = (-1/3)x + 7
Therefore, the equation of the line that goes through the point (6, 5) and is perpendicular to the line y = 3x + 8 is y = (-1/3)x + 7.