Math Problem Statement
write the equation of the line in slope intercept form that passes through the point (-3,7) and (5,3)
Solution
To find the equation of the line in slope-intercept form that passes through the points and , follow these steps:
Step 1: Find the slope of the line.
The slope is given by the formula:
Substituting the given points and :
Step 2: Use the point-slope form of the equation.
Now, use the point-slope form of the line equation:
Using the slope and one of the points, say :
Step 3: Simplify to get the slope-intercept form.
Distribute and simplify the equation:
Add 7 to both sides to solve for :
So, the equation of the line in slope-intercept form is:
Would you like further details or have any questions?
Here are some related questions you might find useful:
- How do you find the slope-intercept form given two points?
- How do you convert a point-slope equation to slope-intercept form?
- What is the significance of the slope in a linear equation?
- How do you determine if two lines are parallel?
- How can you find the y-intercept if the equation is given in standard form?
Tip: The slope-intercept form is useful for quickly identifying the slope and the y-intercept of a line.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Slope-Intercept Form
Formulas
Slope formula m = (y2 - y1) / (x2 - x1)
Slope-intercept form y = mx + b
Point-slope form y - y1 = m(x - x1)
Theorems
-
Suitable Grade Level
Grades 8-10
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