Answer
Full Solution Locked
Sign in to view the complete step-by-step solution and unlock all study resources.
Step 1:: Identify the given information and the equation to solve.
where m is the slope of the line, and $$(x_1, y_1)$$ is a point on the line.
We are given that the points (3, x) and (10, 2) lie on the same line, and we need to find the value of x. The equation of a line can be written in point-slope form as:
Step 2:: Find the slope of the line.
m = \frac{2 - x}{10 - 3} = \frac{2 - x}{7}
First, find the slope of the line using the formula: Using the points (3, x) and (10, 2), we can calculate the slope:
Step 3:: Write the equation of the line in point-slope form.
y - x = \frac{2 - x}{7}(x - 3)
Now, we can write the equation of the line in point-slope form using either of the given points. We'll use the point (3, x):
Step 4:: Solve for y.
y = \frac{6 - 3x}{7} + x
Now, add x to both sides to isolate y:
Step 5:: Simplify the equation.
y = \frac{6 + 4x}{7}
Combine the fractions:
Step 6:: Use the fact that (3, x) lies on the line to find the value of x.
x = 2
Since the point (3, x) lies on the line, we can substitute 3 for x in the equation: Now, solve for x by multiplying both sides by 7 to eliminate the denominator: Subtract 4x from both sides: Finally, divide both sides by 3:
Final Answer
The value of x is 2.
Need Help with Homework?
Stuck on a difficult problem? We've got you covered:
- Post your question or upload an image
- Get instant step-by-step solutions
- Learn from our AI and community of students