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

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

Slope intercept form: y=3/4x+19/4color(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 :"

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