need help on these questions Write the equation of the line that passes through the given point and is perpendicular to the given line. Your answer should be written in slope-intercept form.
P(3, −4), x = − 7/8y + 3
2.Write an equation of a line that passes through the two given points. Your answer should be written in slope-intercept form.
P(6, 0), Q(7, −5)
3.Write an equation of the line with the given properties. Your answer should be written in standard form.
m is undefined passing through P(−7, −9) please just dont leave me with a half answer
1. To find the equation of a line that is perpendicular to a given line, you need to determine the slope of the given line and then take the negative reciprocal of that slope. After that, you can use the point-slope form or convert it to the slope-intercept form.
Given line: x = -(7/8)y + 3
To find the slope of this line, you can rewrite it in slope-intercept form (y = mx + b). Rewrite the given line:
x = -(7/8)y + 3
Multiply both sides by 8 to get rid of the fraction:
8x = -7y + 24
Rearrange terms:
7y = -8x + 24
Divide both sides by 7:
y = (-8/7)x + (24/7)
The slope of the given line is -8/7. The slope of a line perpendicular to this one will be the negative reciprocal, which is 7/8. Now use the point-slope form to find the equation:
Point: P(3, -4)
Slope: 7/8
y - y1 = m(x - x1)
y - (-4) = (7/8)(x - 3)
Simplify:
y + 4 = (7/8)(x - 3)
Lastly, convert it to slope-intercept form (y = mx + b):
y + 4 = (7/8)x - (7/8)3
y + 4 = (7/8)x - 21/8
y = (7/8)x - 21/8 - 32/8
y = (7/8)x - 53/8
Therefore, the equation of the line that passes through point P(3, -4) and is perpendicular to the line x = -(7/8)y + 3 is y = (7/8)x - 53/8 in slope-intercept form.
2. To find the equation of a line passing through two given points, you can apply the formula for slope (m) and then use the point-slope form or convert it to the slope-intercept form.
Given points: P(6, 0), Q(7, -5)
To find the slope (m), use the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the values from the points:
m = (-5 - 0) / (7 - 6)
m = -5
Now use the slope-intercept form to find the equation:
Point: P(6, 0)
Slope: -5
y - y1 = m(x - x1)
y - 0 = -5(x - 6)
Simplify:
y = -5(x - 6)
y = -5x + 30
Therefore, the equation of the line passing through points P(6, 0) and Q(7, -5) is y = -5x + 30 in slope-intercept form.
3. When the slope (m) is undefined, it means the line is a vertical line. A vertical line has the equation of the form x = c, where c is a constant. To find the equation of the line passing through P(-7, -9), you can use the x-coordinate of the point as the constant in the equation:
x = -7
Therefore, the equation of the line with an undefined slope passing through P(-7, -9) is x = -7, written in standard form.