Write the slope intercept equation for the line that passes through (14,-2) and is perpendicular to 7x-10y=18
y = m x + b
to get slope first find slope of given line
10 y = 7 x - 18
y = 0.7 x - 1.8
so slope of given line is 7/10
so slope of our line m = -10/7
so our line is
y = -10 x/7 + b
now find b from given point
-2 = -10*14/7 + b
-2 = -20 + b
b = 18
so
y = (-10/7) x + 18
To find the slope-intercept equation for a line that is perpendicular to another line, we need to follow a few steps:
1. First, determine the slope of the given line. To do this, we need to rearrange the equation of the given line into slope-intercept form (y = mx + b), where 'm' represents the slope.
Given line: 7x - 10y = 18
Rearrange the equation to isolate y:
-10y = -7x + 18
y = (7/10)x - 18/10
y = (7/10)x - 9/5
The slope 'm' of the given line is 7/10.
2. To find the slope of the line perpendicular to the given line, we can use the property that the product of the slopes of two perpendicular lines is -1. So, the slope of the new line will be the negative reciprocal of the slope of the given line.
The given slope is 7/10, so the slope of the new line will be -10/7.
3. Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line passing through the point (14, -2). The point-slope form is given by: y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope.
Plugging in the values from the given point and the slope we found, we get:
y - (-2) = (-10/7)(x - 14)
y + 2 = (-10/7)(x - 14)
4. Finally, we can rearrange the equation into slope-intercept form (y = mx + b) by simplifying the right side:
y + 2 = (-10/7)x + 20
y = (-10/7)x + 20 - 2
y = (-10/7)x + 18
So, the slope-intercept equation for the line passing through the point (14, -2) and perpendicular to the line 7x - 10y = 18 is y = (-10/7)x + 18.