(-(2)/(3), (7)/(8)),3x + 4y = 7

Question

a. Write the slope-intercept form of the equation of the line through the given point and parallel to the given line. b. Write the slope-intercept form of the equation of the line through the given point and perpendicular to the given line.

(-(2)/(3), (7)/(8)), 3x + 4y = 7

Answer 1

3x+4y = 7. solve for y

4y=-3x +7

y = -3x/4 + 7/4 the slope = the coefficient of the x term when the equation is solved for y. the slope=-3/4 =m. any line parallel to the given line has the same slope.

y=mx+b

y=-3x/4 + b. solve for b= y intercept by plugging in the point (-2/3, 7/8)

7/8 =-(3/4)(-2/3) + b= 1/2 + b

b = 7/8 -1/2 = 3/8

y=(-3/4)x +3/8 is the parallel line through the given point, in slope intercept form

for the perpendicular line the slope is the negative inverse of -3/4. Just change the sign and flip the fraction upside down, to get +4/3= m

y=mx +b is the standard equation in slope intercept form

y= 4x/3 + b. to find b which is the intercept, plug in the point (-2/3, 7/8)

7/8 = (4/3)(-2/3) + b

b = 7/8 +8/9 = (63+64)/72 = 127/72

the equation for the perpendicular line in slope intercept form is

y=4x/3 + 127/72

Answer 2

Hello Kaz,

a. For the line to be parallel the slope of both lines have be same. The equation given to you is in standard form. So, first bring the equation in slope-intercept form.

3x + 4y = 7

-3x          -3x

________________

4y = -3x + 7

(4y)/4 = (-3x + 7)/4

y = (-3/4)x + 7/4     --------(slope-intercept form)

Slope is -3/4 and line passes through the point (-2/3, 7/8). Use your point-slope formula.

y - y₁ = m(x - x₁)

y - 7/8 = -3/4(x - (-2/3))

y = -(-3/4)x + 3/8 --------------------(answer)

b) For line to be perpendicular the slope of line will be negative reciprocal or if you multiply the slope of both lines the result should be -1. So, as we know the slope of the given line is -3/4. Slope of perpendicular line will be 4/3. To check mutiply both slopes (-3/4) * (4/3). You'll get -1. Now, that we've got the slope 4/3 and passes through points (-2/3, 7/8). Again use the point-slope formula

y - y₁ = m(x - x₁)

Sustitute, the values and solve. You'll get the answer.

Good luck.