is y=2x-8 and 7x-5y=7 parallel, perpendicular, or neither?

Question

Please show steps and draw the graph. Thanks!!!!

Answer 1

The given equations are      y  = 2x - 8 ;  7x - 5y = 7

y = 2x - 8 ---- (1)   :   7x - 5y = 7 ---- ( 2 )

write the equation (1) in slope intercept form

the slope intercept form y = mx + b

the equation (1) is already in slope intercept form

here slope m = 2

write the equation (2)  in slope intercept form

y = 7/5x - 7/5

here slope m = 7/5

weather check the slopes are equal or opposite reciprocal

if slopes are equal then lines are parallel

if slopes are opposite reciprocal then lines are perpendicular

here the two slopes are neither equal nor opposite reciprocal 

So, here two lines are neither parallel nor perpendicular.

 

Answer 2

Slope - intercept form line equation is y = mx + b, where m is slope and b is y - intercept.

The two equations are : y = 2x - 8 → (1)

                                  7x - 5y = 7 → (2).

First, write the eq'n s (1) and (2) in slope - intercept  form.

Equation (1) : y = 2x - 8.

It is already in slope - intercept  form.

Compare the above equations in slope - intercept form of a line equation.

Slope m₁ = 2. and m₂ = 2.

Equation (2) : 7x - 5y = 7.

5y = 7x - 7

y = (7/5)x - (7/5).

Compare the above equations in slope - intercept form of a line equation.

Slope m₂ = 7/5.

Observe the two slopes, the two lines have different slopes and does not reciprocals to each other.

So, the given lines are neither parallel nor perpendecular.

Observe the graph :

• First line equation is y = 2x - 8.

Write the equation in slope - intercept form y = mx + b, where m is slope and b is y - intercept.

It is already in slope - intercept form.

Compare the equation with slope - intercept form y = mx + b.

slope = 2 and y -intercept is - 8.

y -intercept is - 8, so the line crosses the y - axis at (0, - 8).

Using slope find the next point.

Slope = rise/run = 2/1.

Start at point (0, - 8), move 2 units up and 1 unit right, then plot the point (1, - 6).

• Second line equation is 7x - 5y = 7.

Write the equation in slope - intercept form y = mx + b, where m is slope and b is y - intercept.

5y = 7x - 7

y = (7/5)x - (7/5).

Compare the equation with slope - intercept form y = mx + b.

slope = 7/5 and y -intercept is - 7/5.

y -intercept is - 7/5, so the line crosses the y - axis at (0, - 7/5).

Using slope find the next point.

Slope = rise/run = 7/5.

Start at point (0, - 7/5), move 7 units up and 5 units right, then plot the point (5, 28/5 ).

Draw the two lines through the corresponding points.

Graph :