Write the slope intercept equation for the line that passes through (14,-2) and is perpendicular to 7x-10y=18.Please show work.
graphs of the equations of the system
Ax – 4y = 9
4x + By = –1
is (–1, –3).
To find the slope intercept equation of a line, we need to determine the slope and the y-intercept.
First, let's rewrite the given equation in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
The original equation is 7x - 10y = 18.
To isolate y, we'll subtract 7x from both sides:
-10y = -7x + 18
Next, we divide every term by -10 to solve for y:
y = (7/10)x - 9/5
The slope of the original equation is 7/10.
Since we are looking for a line perpendicular to this line, we know that the slope of the new line will be the negative reciprocal of 7/10.
To find the negative reciprocal, we flip the fraction and change the sign:
Slope of the new line = -10/7.
Now, we have the slope of the new line, but we still need to find the y-intercept (b). To do this, we use the given point (14, -2).
The slope-intercept form of a line is given as: y = mx + b.
We substitute the values into the equation:
-2 = (-10/7)(14) + b
Now, let's solve for b:
-2 = -20 + b
b = -2 + 20
b = 18
Therefore, the y-intercept (b) is 18.
Now that we have the slope (-10/7) and the y-intercept (b = 18), we can write the slope-intercept equation for the line that passes through (14, -2) and is perpendicular to 7x - 10y = 18:
y = (-10/7)x + 18