SOLUTION: Write the slope intercept form of the equation of the line through the given point with the given slope. through:(1,2), slope=7

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Question 224824: Write the slope intercept form of the equation of the line through the given point with the given slope.
through:(1,2), slope=7
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Write the slope intercept form of the equation of the line through the given point with the given slope.
through:(1,2), slope=7

Step 1. The slope-intercept form is given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b).

Step 2. Now we have to find the line with slope m=7 going through point (1,2).

Step 3. Given two points (x1,y1) and (x2,y2), then the slope m is given as

m=%28y2-y1%29%2F%28x2-x1%29

Step 4. Let (x1,y1)=(1,2) or x1=1 and y1=2. Let other point be (x2,y2)=(x,y) or x2=x and y2=y.

Step 5. Now we're given m=7. Substituting above values and variables in the slope equation m yields the following steps:

m=%28y2-y1%29%2F%28x2-x1%29

7=%28y-2%29%2F%28x-1%29=%28y-2%29%2F%28x-1%29

Step 6. Multiply x-1 to both sides to get rid of denominator on right side of equation.

7%28x-1%29=y-2

7x-7=y-2

Step 7. Add 2 to both sides of the equation

7x-7%2B2=y-2%2B2

7x-5=y

Step 7. ANSWER: The equation in slope-intercept form is y=7x-5 where the slope m=7 and the y-intercept b=-5.

Note: the above equation can be rewritten in standard form as

-7x%2By=-5

And the graph is shown below which is consistent with the above steps.

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation -7+x+%2B+1+y+=+-5 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+--7%2F1.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. -5/-7 = 0.714285714285714.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is -5/1 = -5.
  • Slope is --7/1 = 7.
  • Equation in slope-intercept form: y=7*x+-5.



I hope the above steps and explanation were helpful.

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And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV