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Write the slope intercept form of the equation of the line through the given point with the given slope.
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=1/2 going through point (3,1).
Step 3. Given two points (x1,y1) and (x2,y2), then the slope m is given as
Step 4. Let (x1,y1)=(3,1) or x1=3 and y1=1. Let other point be (x2,y2)=(x,y) or x2=x and y2=y.
Step 5. Now we're given
. Substituting above values and variables in the slope equation m yields the following steps:
Step 6. Multiply x-3 to both sides to get rid of denominator on right side of equation.
Step 7. Add 1 to both sides of the equation
Step 7. ANSWER: The equation in slope-intercept form is
where the slope m=1/2 and the y-intercept b=-1/2.
Note: the above equation can be rewritten in standard form as
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 describes a sloping line. For any |
equation ax+by+c = 0, slope is .
- X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. -1/-1 = 1.
- Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is -1/2 = -0.5.
- Slope is --1/2 = 0.5.
- Equation in slope-intercept form: y=0.5*x+-0.5.
I hope the above steps and explanation were helpful.
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