Write the Equation of a line that passes through (4,7) and has slope of -3/4

Question

I have to write the slope, and also use point slope to write as my answers

Answer 1

Hello, thank you for taking the time to post your question!

The underlying equation that you want to use here is the point-slope form of a linear equation:

y−y1​=m(x−x1​)

For this set of values, we have a slope m=−3/4 and a point (x1​,y1​)=(4,7).

Plugging these values into the point-slope equation gives you: y−7=−3/4(x−4)

Solving that algebraically for the value of “y” to put it into the slope-intercept form (y=mx+b) yields: y−7=−3/4x+3

y=−3/4x+3+7

y=−3/4x+10

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Hi Andrew;

The point-slope formula is as follows...

y-y₁=m(x-x₁)

m=slope

Let's plug-in...

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

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

Let's add 7 to both sides of the equation...

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

y=(-3/4)x+10

 

Answer 3

Try this: 

 

Slope intercept form is y = mx + b ;  m = slope.

 

y = -3/4x +b

 

If it passes through (4,7), plug those numbers in, 4 for x and 7 for y to find b (the constant)

 

7 = -3/4 (4) + b

7 = -3 + b   Remember -3/4 * 4 = -3/4 * 4/1 (whole number converts to fraction by dividing by 1)

 

Add 3 to each side to get your constant "b".

 

b = 10

 

y = -3/4 x + 10

 

Knowing the slope intercept form is faster than figuring it out from the definition of slope.  Slope requires knowing 2 points, not just one.  The slope intercept form is easier to memorize and requires only two pieces of information - the slop and ONE point on the line.