_{1}- y

_{2}) / (x

_{1 }- x

_{2}) = (2 - 8) / (-6 - 4) = -6 / -10 = 3/5

is this line that passes through (-6,2) and (4,8)parallel to the line -3x+5y=15?

Tutors, sign in to answer this question.

Thomas L. | Mathematics TutorMathematics Tutor

parallel lines have equal slopes. Find the slope of each and compare.

to find the slope between 2 points: use slope formula (y_{1}- y_{2}) / (x_{1
}- x_{2}) = (2 - 8) / (-6 - 4) = -6 / -10 = 3/5

to find the slope of a line that is already an equation, change the equation to slope intercept form y = mx +b

Solve for y: -3x + 5y = 15 first add 3x to BOTH SIDES of the equals sign. It will cancel on the left and then say 15 + 3x on the right. so the equation is now written as 5y = 15 + 3x. I'm going to switch the -3x and 15 around because usually the form has the "x" term right after the equals sign and the constant number after that. so 5y = 3x +15.

Now divide everything by 5, everything. The 5's cancel on the left and we do a little math on the right to clean up.

y = 3/5 x +3. When in slope intercept form, the "m" is the slope and it is always the number in front of the x(called the coefficient). Our m = 3/5

does 3/5 = 3/5? Yes so the lines are parallel.

**Thanks Krill! I didn't see my mistake till you pointed it out! I fixed it!

This is easily solved if you know vectors. Vector from (-6,2) to (4,8) has coordinates (4-(-6), 8-2)=(10,6). In the line equation ax+by=c coefficients a and b are coordinates of a vector perpendicular to the line. In your case it is vector (-3,5). If the vector from (-6,2) to (4,8) is perpendicular to the vector, perpendicular to the line -3x+5y=15, then it means it is parallel to the line itself, and so is the line passing through those points. Form a scalar product of two vectors:

(10,6)•(-3,5)=10*(-3)+6*5=-30+30=0. Since scalar product of two vectors is zero, they are indeed perpendicular to each other and the line through points is parallel to the line -3x+5y=15. **Answer: yes**.

Alternatively, write your line equation in the slope-intercept form:

-3x+5y=15 ⇔ y=3/5x+3; Slope is 3/5. Find the slope of the line passing through the points (-6,2) and (4,8).

slope=(difference in y coordinates)/(difference in x coordinates)=(8-2)/(4-(-6))=6/10=3/5. Lines have equal slopes, thus it means they are parallel. **Answer: yes.**

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.

Belinda G.

Experienced Elementary School Tutor

$9.75 per 15 min

View Profile >

Ryan K.

Highly Experienced SAT, Chemistry, and Math Tutor

$9.50 per 15 min

View Profile >

Haroldo S.

Biomedical Engineer (UC Berkeley PhD) for Math and Science Tutoring

$12.50 per 15 min

View Profile >

## Comments

_{2 }- y1)/(x_{2}-x_{1})