A line passes through point (3, 7) and has a slope of #3/4#. What is the equation of this line?

2 Answers
May 4, 2017

Answer:

Point slope form: #y-7=3/4(x-3)#

Slope intercept form: #y=3/4x+19/4##color(white)(..)"or"color(white)(..)##y=3/4x+4 3/4#

Explanation:

Since you have one point and the slope, you can use the point slope formula, then solve for #y# to get the slope intercept form, so that you can determine the y-intercept #(b)#. Then you can graph the resulting equation.

Point slope formula
#y-y_1=m(x-x_1)#, where #x_1,y_1=(3,7)#, and #m=3/4# is the slope.

Substitute the given values into the formula.

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

Expand.

#y-7=3/4x-9/4#

Solve for #y# to get the slope intercept form: #y=mx+b#, where #m=3/4# is the slope and #b# is the y-intercept.

#y-7=3/4x-9/4#

Add #7# to both sides.

#y-color(red)cancel(color(black)(7))+color(red)cancel(color(black)(7))=3/4x-9/4+7#

Simplify.

#y=3/4x-9/4+7#

In order to add and subtract fractions, they must have the same denominator. #7=7/1# and can be multiplied by the equivalent fraction #color(red)(4/4)# in order to get the same denominator as #9/4#.

#y=3/4x-9/4+7/1xxcolor(red)(4/4)#

Simplify.

#y=3/4x-9/4+28/4#

Simplify.

#y=3/4x+19/4# or

#y=3/4x+4 3/4#

The y-intercept is #19/4#

graph{y=3/4x+19/4 [-17.42, 14.6, -5.96, 10.06]}

May 4, 2017

Answer:

#"answer :"#

#y=3/4x-37/4#

#"Or "#

#-3x+4y=-37#

Explanation:

#"equation for solution is "#

#y-y_1=m(x-x_1)#

#"where " P(x_1,y_1)=P(3,7)#

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

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

#y=3/4x-9/4+7#

#y=3/4x-37/4#

#"Or "#

#y-3/4x=-37/4#

#(4y-3x)/4=-37/4#

#(4y-3x)/cancel(4)=-37/cancel(4)#

#-3x+4y=-37#