Write the equation of a line in slope intercept form that contains (3/4, 1/2) and has the same slope as the line described by y + 3x = 6.
y = -3 x + 6, slope = -3
(y-1/2)/(x-3/4) = -3
y - 1/2 = -3x + 9/4
y = -3 x + 11/4
pls be a little more through (sorry was taking a poo)
follow me on discord its nom-nom#7038
To find the equation of a line in slope-intercept form, we need two pieces of information: the slope of the line and a point that lies on the line.
Let's start by finding the slope of the line described by y + 3x = 6.
To get the equation in slope-intercept form (y = mx + b), we isolate y by subtracting 3x from both sides of the equation:
y = -3x + 6
From this equation, we can see that the slope (m) of the line is -3.
Next, we use the given point (3/4, 1/2) that lies on the line. We can substitute the coordinates of the point into the slope-intercept form equation and solve for the y-intercept (b).
Using the slope-intercept form equation, y = mx + b, we substitute the slope (-3) and the x-coordinate (3/4) and the y-coordinate (1/2) of the given point:
1/2 = -3(3/4) + b
Simplifying this equation, we have:
1/2 = -9/4 + b
To solve for b, we can add 9/4 to both sides of the equation:
1/2 + 9/4 = b
To find the common denominator, we can multiply 1/2 by 2/2 to get 2/4:
2/4 + 9/4 = b
Combining the fractions gives us:
11/4 = b
So, the y-intercept (b) is 11/4.
Finally, we can write the equation of the line with the same slope as y + 3x = 6 and containing the point (3/4, 1/2) in slope-intercept form.
y = mx + b
Substituting the slope (-3) and the y-intercept (11/4), we have:
y = -3x + 11/4
Therefore, the equation of the line is y = -3x + 11/4 in slope-intercept form.