write an equation of the line passing through the point (8,7) that is perpendicular to the line y+7=-7/17(x+8)
y=7/17x+7
y=17/7x-87/7
To find the equation of a line that is perpendicular to another line, we need to determine the slope of the given line first. The given line is in the form y + 7 = (-7/17)(x+8).
By comparing this equation with the slope-intercept form y = mx + b, we can see that the slope (m) of the given line is -7/17.
Since a line that is perpendicular to another line has a slope that is the negative reciprocal of the original slope, the slope of the perpendicular line will be the opposite sign and the reciprocal of -7/17.
The negative reciprocal of -7/17 is 17/7. Therefore, the slope (m) of the line we are looking for is 17/7.
Now that we have the slope, we can write the equation of the line using the point-slope form:
y - y₁ = m(x - x₁),
where (x₁, y₁) is the given point (8,7), and m is the slope 17/7.
Plugging in the values, we get:
y - 7 = (17/7)(x - 8).
Expanding the equation, we have:
y - 7 = (17/7)x - 17(8/7).
Simplifying further, we have:
y - 7 = (17/7)x - 136/7.
To get the equation in the form y = mx + b (slope-intercept form), we need to isolate y. Thus, we can add 7 to both sides of the equation:
y = (17/7)x - 136/7 + 7.
Combining like terms, we have:
y = (17/7)x - 136/7 + 49/7.
Simplifying:
y = (17/7)x - 87/7.
Therefore, the equation of the line passing through the point (8,7) that is perpendicular to the line y + 7 = (-7/17)(x + 8) is y = (17/7)x - 87/7.
y = -(7/17)x + some old constant
slope m = -7/17
slope of perpendicular = -1/m = 17/7
y = 17 x/7 + b
7 = 17*8/7 + b
49 = 136 + 7 b
7b = -87
b = -87/7
7 y = 17 x - 87